Question

23. In PQR if <P - Q = 42°and <Q -<R =21 then the measure of 2 Q is :- a) 53 (b)63 (c)32 (d) 95​

Answer 1

Answer:

53 cm

Step-by-step explanation:

It is given that ∠P−∠Q=42  

∘

 

It can be written as

∠P=42   +∠Q

We know that the sum of all the angles in a triangle is 180  

∘

.

So we can write it as

∠P+∠Q+∠R=180  

 

By substituting ∠P=42  

+∠Q in the above equation

42  

+∠Q+∠Q+∠R=180  

 

On further calculation

42  

+2∠Q+∠R=180  

 

2∠Q+∠R=180  

−42  

 

By subtraction we get

2∠Q+∠R=138  

It is given that ∠Q−∠R=21  

 

It can be written as

∠R=∠Q−21  

 

By substituting the value of ∠R in equation (i)

2∠Q+∠Q−21  

=138  

 

On further calculation

3∠Q−21  

=138  

3∠Q=138  

∘

+21  

 

By addition

3∠Q=159  

By division

∠Q=159/3

∠Q=53