△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 (denoted as \( \triangle XYZ \sim \triangle RST \)), their corresponding angles are equal.

Given:

  • \( m\angle X = 50^\circ \)
  • \( m\angle S = 79^\circ \)

To find the measure of angle \( T \), we first calculate the measure of angle \( Y \) in triangle \( XYZ \).

The sum of the angles in a triangle is \( 180^\circ \). Therefore,

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

However, we need \( m\angle R \) in triangle \( RST \) which would correspond to angle \( Y \) in triangle \( XYZ \).

Since angle \( S \) corresponds to angle \( Y \) due to similarity, we have:

\[ m\angle Y = m\angle R = 79^\circ \]

Now we can calculate \( m\angle T \):

Using the triangle angle sum for triangle \( RST \):

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

Substituting the known values:

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

This simplifies to:

\[ m\angle T = 180^\circ - 79^\circ - 50^\circ \] \[ m\angle T = 180^\circ - 129^\circ \] \[ m\angle T = 51^\circ \]

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

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