△XYZ∼△RST. m∠X=50°, m∠S=79°. What is the measure of angle T?
To find the measure of angle T, we first need to find the scale factor between the two triangles.
We can use the given angle measurements to set up a proportion:
m∠X / m∠S = m∠Y / m∠T
Substitute the given values:
50° / 79° = m∠Y / m∠T
Solve for m∠Y:
m∠Y = (50/79) * m∠T
Now, since the sum of angles in a triangle is 180°, we can find m∠Y:
m∠X + m∠Y + m∠Z = 180°
50° + m∠Y + m∠Z = 180°
m∠Y = 180° - 50° - m∠Z
Substitute the equation above:
(50/79) * m∠T = 180° - 50° - m∠T
Simplify:
(50/79) * m∠T = 130° - m∠T
Now, solve for m∠T:
(50/79 + 1) * m∠T = 130°
(129/79) * m∠T = 130°
m∠T = 130° * (79/129)
m∠T ≈ 79.22°
Therefore, the measure of angle T is approximately 79.22°.