Question

In the adjoining figure, p ∥ q. Find the unknown angles.

Find the value of C.

• A. 90${}^{\circ }$
• B. 120${}^{\circ }$
• C. 55${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

The correct option is C 55${}^{\circ }$

By observing the figure,
∠d = ∠125${}^{\circ }$ … [∵ corresponding angles]
We know that the sum of the adjacent angles of a linear pair is 180${}^{\circ }$.
Then,
= ∠e + 125${}^{\circ }$ = 180${}^{\circ }$ … [linear pair]
= ∠e = 180${}^{\circ }$ – 125${}^{\circ }$
= ∠e = 55${}^{\circ }$
From the rule of vertically opposite angles,
∠f = ∠e = 55${}^{\circ }$
∠b = ∠d = 125${}^{\circ }$
By the property of corresponding angles,
∠c = ∠f = 55v
∠a = ∠e = 55${}^{\circ }$