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Find all unknown angle measures in the pair of similar triangles.

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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

Nov 30, 2017

#1
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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°

Nov 30, 2017

#1
+7348
+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