In the diagram, angletrv ≅ anglevrw. 2 lines intersect. a line with points t, r, w intersects a line with points s, r, v at point r. what is the measure of anglesrt? manglesrt = degrees

The measure of angle TRV is 130° ⇒ last answer

Step-by-step explanation:

* According to the attached graph

- Line TRW intersects line SRV at point R

- The measure of angle VRT is (2x + 10)°

- The measure of angle VRW is (x - 10)°

- We need to find measure of angle TRV

- From the attached figure

∵ T , R , W lie on the same line

∴ ∠TRW is a straight angle

- The measure of the straight angle is 180°

∴ m∠TRW = 180°

∵ ∠TRW contains ∠VRT and ∠VRW

∴ m∠VRT + m∠VRW = m∠TRW

∴ m∠VRT + m∠VRW = 180°

∵ m∠VRT = (2x + 10)°

∵ m∠VRW is (x - 10)°

∴ 2x + 10 + x - 10 = 180

- Add like terms

∴ 3x = 180

- Divide both sides by 3

∴ x = 60

∵ m∠TRV = (2x + 10)°

- Substitute x by 60

∴  m∠TRV = 2(60) + 10 = 120 + 10 = 130°

∴ The measure of angle TRV is 130°