Question triang

4.1 Lines, Angles, and Triangles - Triangle sum theorem
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  • Triangle upper R upper T upper U is labeled as follows:
    • The measure of angle upper R upper T upper U is x/li>
  • The 2 triangles partially overlap:
    • Side upper R upper T of triangle upper R upper T upper U intersects side upper S upper V of triangle upper S upper V upper U.
    • Vertex upper V of triangle upper S upper V upper U lies on side upper R upper U of triangle upper R upper T upper U.
    • Vertex upper T of triangle upper R upper T upper U lies on side upper S upper U of triangle upper S upper V upper U.
  • A note indies the figure is not drawn to scale.

 

In the figure, RT=TU, the measure of angle VST is 29°, and the measure of angle RVS is 41°. What is the value of x ?

Enter your answer:

Triangle upper R upper T upper U is labeled as follows: The measure of angle upper

Hard-difficulty · SAT Math · Lines, Angles, and Triangles — Triangle sum theorem. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

The correct answer is 156 . In the figure shown, the sum of the measures of angle UVS and angle RVS is 180°. It’s given that the measure of angle RVS is 41°. Therefore, the measure of angle UVS is 180-41°, or 139°. The sum of the measures of the interior angles of a triangle is 180°. In triangle UVS, the measure of angle UVS is 139° and it's given that the measure of angle VST is 29°. Thus, the measure of angle VUS is 180-139-29°, or 12°. It’s given that RT=TU. Therefore, triangle TUR is an isosceles triangle and the measure of VUS is equal to the measure of angle TRU. In triangle TUR, the measure of angle VUS is 12° and the measure of angle TRU is 12°. Thus, the measure of angle UTR is 180-12-12°, or 156°. The figure shows that the measure of angle UTR is x°, so the value of x is 156 .