Linear Pairs and Vertical Angles

Given: m∠ELG = 124° Prove: x = 28 Complete the steps in the two-column proof.

(THESE WERE THE ONLY GIVEN ONE'S) 4. (reasons) club: angle addition postulate 6. (statement) diamond: 2x=56

Given: m∠QVR = 49° Prove: x = 15 3 lines are shown. A horizontal line with points Q, V, T intersects with a line with points R, V, U at point V. A line extends vertically from point V to point S. Angle T V U is (3 x + 4) degrees. Complete the steps of the proof.

(THESE WERE THE ONLY GIVEN ONE'S) 6. (statement) diamond: 3x+4=49 4. (reasons) club: vertical angles theorem

Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.

Sample Response: If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.

3 lines are shown. A line with points C, A, F intersects a line with points B, A, E at point A. A line extends from point A to point D between angle C A E. Angle C A D is 89 degrees and angle B A F is 134 degrees. What is the measure of ∠DAE?

a. 45 degrees

Which angles are linear pairs? Check all that apply. ∠SRT and ∠TRV ∠SRT and ∠TRV ∠VRW and ∠WRS ∠VRU and ∠URS ∠URW and ∠WRS.

a. ∠SRT and ∠TRV c. ∠VRW and ∠WRS d. ∠VRU and ∠URS

2 lines intersect. A line with points T, R, W intersects a line with point S, R, V at point R. 4 angles are created. Labeled clockwise, from the top: (3 x) degrees, blank, blank, x degrees. What is the value of x?

b. 45

4 lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Another line extends from point R to point U in between angle V R W. Which is a pair of vertical angles?

b. ∠TRS and ∠VRW

3 lines are shown. A line with points T, R, W intersects a line with points S, R, W at point R. Another line extends from point R to point U between angle T, R, V. Angle V R W is (3 x) degrees and angle T R S is (2 x + 18) degrees. What is m∠SRW?

c. 126

If the m∠SRW = 85°, what are the measures of ∠VRU and ∠URW?

m∠VRU = 80 degrees & m∠URW = 15 degrees