NTSE Stage 2 SAT 2018 Exam Question Paper

Question : 55 of 100

Marks: +1, -0

In ∆ABC, AB = AC, P and Q are points on AC and AB respectively such that BC = BP = PQ = AQ. Then, ∠AQP is equal to (use π =180º)

Solution:

AB=AC

⇒∠C=∠B

⇒∠B=∠C=a

By angle sum properly in ∆ABC,

{b}+{a}+{a}=180

.......(1)
In ΔQPB

⇒∠{QPB}=180-4{b}

Since ‘APC’ is a straight line

⇒180-4b+a+b=180

⇒a=3b

.....(2)
From equation (1) & (2)

b+2(3b)=180

b=180/7

∠{AQP}=180^{∘}-2(\;\;{180}/{7})=\;\;{5}/{7}π

Go to Question:

Prev Question

Next Question