The sum of all 8 interior angles is given by . Since each interior angle has the same measure, we divide by 8 to find the measure of one interior angle: . Each exterior angle is supplementary to this and therefore must have measure 45º. The diagram given below shows a regular pentagon. If point O is the center, what are the measures of angles ... 180(n − 2) = 180(6 − 2) = 720 ∘. We know that the sum of all the interior angles in this polygon is equal to 720 degrees. The sum of all the angles of the given polygon is: ∠A + ∠B + ∠C + ∠D + ∠E + ∠F = (x − 60) + (x − 20) + 130 + 120 + 110 + (x − 40) = 3x + 240. Now we set this sum equal to 720 and solve it for x. ∠3 and ∠4 are vertical angles. ∠5 and ∠8 are corresponding angles. ∠3 and ∠5 are alternate interior angles. ∠2 and ∠8 are alternate exterior angles. All of the above are false. 22. The following diagram shows parallel lines cut by a transversal. What is the measure of ∠2? 80° 100° 20° 160° 50° 23.

Consecutive Interior Angles Theorem Name: Prove that if parallel lines are cut by a transversal then consecutive interior angles are supplementary. Given: Lines mand n are parallel. Prove: zl and —2 are supplementary. STATEMENTS I Lines m and n are parallel 3 —3 and —2 area linear pair 4 —3 and —2 are supplementary Improve your math knowledge with free questions in "Identify corresponding and consecutive interior angles" and thousands of other math skills.2. 4 and 1 are supplementary 2. Consecutive Interior Angle Theorem 3. m 4 + m 1 = 180 Definition of supplementary angles 4. m 4 = m 3 4. Definition of congruent angles 5. m 3 + m 1 = 180 5. Substitution 6. 3 and 1 are supplementary Definition of supplementary angles 7. 7.q ║ p If consecutive interior s are

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In consecutive interpretation the interpreter repeats in the target language the passage that the speaker has just said in the source language. • short consecutive - usually only one or two sentences are said and sometimes even a part of a sentence. This mode is more interactive and...Angles 1,2,6,7 are exterior angles Alternate interior angles: Pairs of interior angles on opposite sides of the transversal. For instance, angle 3 and angle 5 are alternate interior angles. Angle 4 and angle 8 are also alternate interior angles. Alternate exterior angles: Pairs of exterior angles on opposite sides of the transversal. Alternate Interior Angles If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. 3 and 6, 4 and 5 Same-Side Interior Angles If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. 3 and 5, 4 and 6 Alternate Exterior Angle Learners determine angle measurement by identifying properties of interior angles, exterior angles, vertical angles and supplementary angles. They justify their answers. This two-page worksheet contains 23 problems. x = 60 by the Consecutive Interior Angles Theorem; y = 10 by the Supplement Theorem PROOF Copy and complete the proof of Theorem 3.2. Given: LVDWUDQVYHUVDO Prove: 1 and 2 are supplementary; 3 and 4 are supplementary. Proof: $16:(5 CCSS ARGUMENTS Write a two -column proof of the Alternate Exterior Angles Theorem. $16:(5 Given: Prove: Consecutive interior angles are supplementary. Consecutive interior angles are interior angles which are on the same side of the transversal line. Alternate interior angles don’t have any specific properties in the case of non – parallel lines. Alternate Interior Angles Theorem then || lines (Corr. Angles Converse) 19) 43; If consecutive interior angles supplementary, then || lines (Consec. Int. Angles Converse) 20) 27; Vertical Angles are congruent and If consecutive interior angles supplementary, then || lines (Consect. Int. Angles Converse) 37) Daniela; ∡1 and ∡2 are alternate interior angles for ̅̅̅̅̅ and ...

If the opposite angles of a quadrilateral are supplementary, then the quadrilateral can be inscribed in a circle. (p. 616). 11.10. If two chords intersect inside a circle, then the measure of each angle formed is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. (p. 620).The courthouse and bank at non-congruent alternate interior angles. A department store and a place of worship at congruent corresponding angles. The fire department and police stations at congruent alternate interior angles. A movie theater and a park at supplementary consecutive exterior angles . Grading Rubric We know that consecutive interior angles of a parallelogram are supplementary. ∴ (x + 60)° + (2x + 30)° = 180°. ⇒ 3x° + 90° = 180°. ⇒ 3x° = 90°. ⇒ x° = 30°. Thus, two consecutive angles are (30 + 60)° , (2 × 30 + 30)° i.e. 90° and 90°. Hence , the special name of the given parallelogram is ractangle. Please log in or register to add a comment. Oct 05, 2019 · One of the basic properties of parallelograms is that any pair of consecutive angles are supplementary. This property will be very useful in many problems involving parallelograms. We’ll prove this property using one of the theorems about parallel lines – the Consecutive Interior Angles Theorem. Same Side Exterior Angles questions. Identify the special name for each angle pair. 10 and 14 a. alternateexterior b. interior c. consecutive interior d. corresponding 34. If ABC is isosceles with vertex angle B, and , which theorem or postulate can be used to prove ? a. SSS b. SAS c. ASA d. AAS Refer to thefigure below answer following questions. 35. Name an altitude ...

C-38 Kite Angle Bisector Conjecture - The vertex angles of a kite are bisected by a diagonal. C-39 Trapezoid Consecutive Angles Conjecture - The consecutive angles between the bases of a trapezoid are supplementary. C-40 Isosceles Trapezoid Conjecture - The base angles of an isosceles trapezoid are congruent. Theorem 3.2: (The Consecutive Interior Angles Theorem) If two parallel lines are cut by a transversal, then Consecutive Interior angles are supplementary . Angle Pairs - review Transversal a line that crosses 2 other lines Angle Pairs Example 3 Identify all pairs of angles of the given type: Corresponding E. Vertical Angles Alternate interior Alternate exterior F. Linear Pairs Consecutive interior GUIDED PRACTICE CHAPTER 3 Parallel and Perpendicular Lines 3.1 IDENTIFY PAIRS OF LINES AND ANGLES ...

Two angles are complementary if the sum of their angles equals 90 o. If one angle is known, its complementary angle can be found by subtracting the measure of its angle from 90 o. Example: What is the complementary angle of 43 o? Solution: 90 o - 43 o = 47 o. Two angles are supplementary if the sum of their angles equals 180 o. 50. 30, 90, 60; By the Interior Angle Sum Theorem, the sum of the interior angles is 720. Since polygon ORSTVXis regular, there are 6 congruent angles. Each angle has a measure of 120. So, mZXOR and mZXVT= 120. Since polygon ORSTVXis regular, XO = QR. By the Isosceles A Theorem, mLOXR mZQRX. The interior angles of a triangle add up to 180, so ... Angle A is 32 degrees so angle B is 148 degrees because they are supplementary angles and supplementary angles add up to 180. Angle G is also 148 degrees because it corresponds with angle B and corresponding angles have the same measure. We will do this lesson in class. We will do this lesson in class. Complementary & Supplementary Angles Quiz Complementary & Supplementary Angles Quiz . Angles Quiz Angles Quiz . ... Consecutive interior. D. Alternate exterior. 24. We have new pairs of corresponding angles. What can be said about the adjacent angles of a parallelogram. Again the parallel line conjectures and linear pairs conjecture can help us. The measures of the adjacent angles of a parallelogram add up to be 180 degrees, or they are supplementary.

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