Question

What is the value of x

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Value of x is 47°

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :- AB parallel to CD

AQP = 78°

CPR = 35°

PRQ = 90°

To find :- Value of x

Solution :-

First find angle QPR

Consider AB parallel to CD and QP as transversal

QPC = AQP (Since Alternate interior angles are equal)

i.e, QPR + CPR = AQP

$\tt{\implies{QPR + 35 = 78}}$

$\tt{\implies{QPR = 78 - 35}}$

$\tt{\implies{QPR = 43}}$

You can find the value of x now

Consider ΔPQR

PQR + PRQ + QPR = 180° (Since Angle sum property of a triangle )

$\tt{\implies{x + 90 + 43 = 180}}$

$\tt{\implies{x + 133 = 180}}$

$\tt{\implies{x=180-133}}$

$\tt{\implies{x = 47 }}$

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Extra info related to the question:-

What are parallel lines ?

Pair of lines in a plane having no common point are called parallel lines .

What is transversal?

A transversal is a line that passes through two lines at two distinct points.