Find all unknown angle measures in the pair of similar triangles. Note that the triangles are not drawn to scale.

Triangles T V W and X Y Z have the same shape and orientation. In triangle T V W, the angles are labeled as follows: T, unlabeled; V, 20 degrees; W, unlabeled. Angle T is marked with one arc and angle V is marked with two arcs. In triangle X Y Z, the angles are labeled as follows: X, 83 degrees; Y, unlabeled; Z, unlabeled. Angle X is marked with one arc and angle Y is marked with two arcs. 20° 83°

Enter the missing angle measures below.

mangle∠Tequals= ____ degrees°

mangle∠Wequals= ______ degrees°

mangle∠Yequals= ____ degrees°

mangle∠Zequals= ______ degrees

ladiikeiii
Nov 30, 2017

#1**+3 **

m∠V = 20°

m∠X = 83°

△TVW is similar to △XYZ . So...

m∠T = m∠X = 83°

So we know two of the angles in △TVW : m∠T = 83° and m∠V = 20° .

Since the sum of the angles in any triangle = 180° ,

the third angle in △TVW , m∠W = 180° - 83° - 20° = 77°

m∠W = 77°

Again, △TVW is similar to △XYZ . So...

m∠Y = m∠V = 20°

m∠Z = m∠W = 77°

hectictar
Nov 30, 2017

#1**+3 **

Best Answer

m∠V = 20°

m∠X = 83°

△TVW is similar to △XYZ . So...

m∠T = m∠X = 83°

So we know two of the angles in △TVW : m∠T = 83° and m∠V = 20° .

Since the sum of the angles in any triangle = 180° ,

the third angle in △TVW , m∠W = 180° - 83° - 20° = 77°

m∠W = 77°

Again, △TVW is similar to △XYZ . So...

m∠Y = m∠V = 20°

m∠Z = m∠W = 77°

hectictar
Nov 30, 2017