Question

△RST is similar to triangle △XYZ by the AA Similarity Postulate .

What is the measure of ∠X?

Answer 1

x = 180 - 23 - 47 = 110

Answer 2

The measure of ∠X is 110°

Explanation:

If two triangles are similar then their corresponding angles are same by AA similarity.

we can observe from provided triangles,

∠S=∠Y=23°

∠T=∠Z=47°

So, In triangle Δ XYZ ;

∠X +∠Y +∠Z = 180° (∵By angle sum property)

∠X +23° +47° = 180°

∠X +70° = 180°

Subtract 70° from both the sides in the above expression,

∠X = 180°-70°

∠X = 110°

Hence the measure of ∠X is 110°