+0  
 
0
45
1
avatar+350 

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

Best Answer 

 #1
avatar+5555 
+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
Sort: 

1+0 Answers

 #1
avatar+5555 
+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

6 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details