△XYZ∼△RST

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

°

1 answer

Since triangles \( ∆XYZ \) and \( ∆RST \) are similar (indicated by \( ∆XYZ ∼ ∆RST \)), their corresponding angles are equal.

We know:

  • \( m∠X = 50° \)
  • \( m∠S = 79° \)

To find \( m∠T \), we first calculate \( m∠Y \) since the angles in a triangle sum to \( 180° \):

\[ m∠Y = 180° - m∠X - m∠Z \]

But we need to find \( m∠Z \) in terms of \( m∠R \) because of the similarity.

Thus:

  • For triangle \( ∆RST \):

\[ m∠R + m∠S + m∠T = 180° \]

So, we need to determine \( m∠R \) based on the corresponding angle \( m∠Y \) from triangle \( ∆XYZ \):

\[ m∠Y = m∠R \]

Now, compute \( m∠Y \):

\[ m∠Y = 180° - m∠X - m∠Z \] However, we do not have \( m∠Z \) directly, so we must sum the known angles.

From \( \triangle RST \):

  • \( m∠R = m∠Y \)
  • \( m∠S = 79° \)

Thus:

\[ m∠Z + m∠Y + m∠S = 180° \] \[ m∠Z + 50° + 79° = 180° \] \[ m∠Z + 129° = 180° \] \[ m∠Z = 51° \]

The last angle is:

\[ m∠T + m∠S + m∠R = 180° \] \[ m∠T + 79° + 51° = 180° \] \[ m∠T + 130° = 180° \] \[ m∠T = 50° \]

Thus, \( m∠T = 50° \).

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

\[ \boxed{50°} \]