Question

△RST is similar to triangle △XYZ by the AA Similarity Postulate.
What is the measure of ∠X?
Enter your answer in the box.

m∠X= ___ °

Answer 1

Answer:

110

Step-by-step explanation:

I took the quiz. I hope this helps :)

Answer 2

The measure of ∠X is 110°.

Similar Triangles

Two triangles are said to be similar triangles if their corresponding angles are similar and their sides are in the ratio. It is denoted by '~'.

Given to us

∠XZY = 47°,

∠RST = 23°,

Similar Triangles

As given to us, $\triangle XYZ \sim \triangle RST$,

∠XYZ = ∠RST = 23°,

∠XZY = ∠RTS = 47°,

∠ZXY = ∠TRS = ∠X,

Sum of all the angles of a triangle

As we know that Sum of all the angles of a triangle is equal to 180°.

therefore, ∠XYZ + ∠XZY + ∠ZXY = 180°,

23° + 47° + ∠X = 180°,

70° + ∠X = 180°

∠X = 180° - 70°

∠X = 110°

Hence, the measure of ∠X is 110°.

Lear more about Similar triangles:

https://brainly.com/question/25882965