Question

a triangle is shown. a side of the triangle lies on line m. select values to complete the sentences to justify the measure of ∠t, in degrees. the sum of the measures of ∠u and ∠v is < >. since the sum of the interior angles of a triangle is < >, ∠t is equal to < >.

Explanation:

Step1: Find the measure of ∠U

Use the linear - pair property. Since an angle and its linear - pair angle sum to 180°, for the angle adjacent to ∠U which is 140°, then ∠U=180 - 140 = 40°.

Step2: Find the measure of ∠V

Use the linear - pair property. Since an angle and its linear - pair angle sum to 180°, for the angle adjacent to ∠V which is 105°, then ∠V=180 - 105 = 75°.

Step3: Find the measure of ∠T

Use the angle - sum property of a triangle. The sum of the interior angles of a triangle is 180°. Let ∠T be the third angle of the triangle. Then ∠T=180-(∠U + ∠V). Substitute ∠U = 40° and ∠V = 75° into the formula: ∠T=180-(40 + 75)=65°.

Answer:

The sum of the measures of ∠U and ∠V is 115°. Since the sum of the interior angles of a triangle is 180°, ∠T is equal to 65°.