Triangle upper R upper T upper U is labeled as follows:

The measure of angle upper R upper T upper U is x/li>

Question

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, $R T = T U$ , the measure of angle $V S T$ is $29 degree$ , and the measure of angle $R V S$ is $41 degree$ . What is the value of $x$ ?

Accepted Answer

The correct answer is 156 . In the figure shown, the sum of the measures of angle U V S and angle R V S is 180 &#176; . It&rsquo;s given that the measure of angle R V S is 41 &#176; . Therefore, the measure of angle U V S is 180 - 41 &#176; , or 139 &#176; . The sum of the measures of the interior angles of a triangle is 180 &#176; . In triangle U V S , the measure of angle U V S is 139 &#176; and it's given that the measure of angle V S T is 29 &#176; . Thus, the measure of angle V U S is 180 - 139 - 29 &#176; , or 12 &#176; . It&rsquo;s given that R T = T U . Therefore, triangle T U R is an isosceles triangle and the measure of V U S is equal to the measure of angle T R U . In triangle T U R , the measure of angle V U S is 12 &#176; and the measure of angle T R U is 12 &#176; . Thus, the measure of angle U T R is 180 - 12 - 12 &#176; , or 156 &#176; . The figure shows that the measure of angle U T R is x &#176; , so the value of x is 156 .

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