Question

Plz tell me the answer of this

Answer 1

GIVEN:-

• $\rm{\angle{QPR}=(2x+2)}$

• $\rm{\angle{PQR}=x}$

• $\rm{\angle{PRQ}=(2x-7)}$.

TO FIND:-

• The value of x and the measure of all the angles in given Figure.

CONCEPT USED:-

• Sum of all the angles in a given triangle is 180°.

Now,

$\implies\rm{\angle{P}+\angle{Q}+\angle{R}=180}$

$\implies\rm{2x+2+2x-7+x=180}$

$\implies\rm{5x-5=180}$

$\implies\rm{5x=185}$

$\implies\rm{x=\dfrac{185}{5}}$

$\implies\rm{x=37}$.

Now, Substitute the value of x

$\implies\sf{(2x-2)=2\times{37}+2}$

$\implies\sf{\angle{P}=76}$

$\implies\sf{x=37}$

$\implies\sf{\angle{Q}=37}$

$\implies\sf{(2x-7)=2\times{37}-7}$

$\implies\sf{\angle{R}=67}$.

Therefore, The Correct answer is A.

VERIFICATION

$\rm{\angle{P}+\angle{Q}+\angle{R}=180}$

$\rm{76+37+67=180}$

$\rm{180=180}$

Hence, Verified ✔️