Question

In Fig., lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to 

(a) 126° (b) 144° (c) 136° (d) 154°

Answer 1

(b) 144^o

Sum of all angle about a straight line given in the figure are equal to 180^o.

PQ is a straight line.

Then, ∠POR + ∠ROT + ∠TOQ = 180^o

Given, x : y = 3 : 2

Let us assume x = 3a, y = 2a

90^o + 3a + 2a = 180^o

90^o + 5a = 180^o

5a = 180^o – 90^o

5a = 90^o

a = 90/5

a = 18^o

So, x = 3a = 3 × 18 = 54^o

Y = 2a = 2 × 18 = 36^o

From the figure SOT is a straight line,

Then, Z + Y = 180^o

Z + 36^o = 180^o

Z = 180^o – 36^o

Z = 144^o