+0  
 
0
56
1
avatar+36 

In the diagram,  if $\angle PQR = 48^\circ$ , what is the measure of $\angle PMN$?

 

Echotastic  Mar 21, 2018
Sort: 

1+0 Answers

 #1
avatar+6949 
+3

Since  QR  =  PR  ,   △PQR  is isoscelese and its base angles are congruent. So...

 

∠PQR   =   ∠RPQ   =   48°

 

And vertical angles are congruent, so...

 

∠RPQ   =   ∠MPN   =   48°

 

Since  MP  =  NP  ,   △MNP  is isoscelese and its base angles are congruent. So...

 

∠PNM   =   ∠PMN

 

Since there are 180°  in every triangle...

 

∠MPN + ∠PMN + ∠PNM  =  180°

                                                         Plug in  48°  for  ∠MPN  and plug in  ∠PMN  for  ∠PNM

48° + ∠PMN + ∠PMN  =  180°

                                                         Combine like terms.

48° + 2(∠PMN)  =  180°

                                                         Subtract  48°  from both sides.

2(∠PMN)  =  132°

                                                         Divide both sides by  2 .

∠PMN  =  66°

hectictar  Mar 21, 2018

25 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