△XYZ∼△RST

. m∠X=50°
, m∠S=79°
. What is the measure of angle T
?(1 point)
m∠T =

°

1 answer

Since triangles \( \triangle XYZ \) and \( \triangle RST \) are similar, the sum of the angles in each triangle must equal \( 180^\circ \).

First, calculate the measure of angle \( Y \) in triangle \( XYZ \):

\[ m\angle Y = 180^\circ - m\angle X - m\angle Z \]

However, we don't have the measure of angle \( Z \) provided. We can solve for angle \( T \) in triangle \( RST \) using the measure of angle \( S \).

Now, in triangle \( RST \):

\[ m\angle R + m\angle S + m\angle T = 180^\circ \]

Given \( m\angle S = 79^\circ \), we need to determine \( m\angle R \) using the corresponding angle in triangle \( XYZ \) due to the similarity of the triangles.

Since \( \triangle XYZ \sim \triangle RST \), the angles \( X \) and \( R \) are corresponding angles. Therefore, we can find \( m\angle R \):

\[ m\angle R = m\angle X = 50^\circ \]

Now we can substitute \( m\angle R \) and \( m\angle S \) back into the equation for triangle \( RST \):

\[ 50^\circ + 79^\circ + m\angle T = 180^\circ \]

\[ 129^\circ + m\angle T = 180^\circ \]

Now, solving for \( m\angle T \):

\[ m\angle T = 180^\circ - 129^\circ = 51^\circ \]

Thus, the measure of angle \( T \) is:

\[ \boxed{51^\circ} \]