+394 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
+9481 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°
+9481 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°
