Question

Two angles are a linear pair. Their measures are represented by x + 30 and 3x - 10 respectively. What are the measures of the angles?

• A. 70${}^{\circ }$ and 110${}^{\circ }$
• B. 60${}^{\circ }$ and 120${}^{\circ }$
• C. 50${}^{\circ }$ and 130${}^{\circ }$
• D. 40${}^{\circ }$ and 140${}^{\circ }$

Answer 1

The correct option is A

70${}^{\circ }$ and 110${}^{\circ }$

The angles are a linear pair, hence the sum of the angles = 180${}^{\circ }$

Therefore,

(x + 30${}^{\circ }$) + (3x - 10${}^{\circ }$) = 180${}^{\circ }$

⇒ 4x + 20${}^{\circ }$ = 180${}^{\circ }$

⇒ 4x = 160${}^{\circ }$

⇒ x = 40${}^{\circ }$

Therefore the measures of the angles are,

⇒ x + 30${}^{\circ }$ = 40${}^{\circ }$ + 30${}^{\circ }$ = 70${}^{\circ }$

⇒ 3x - 10${}^{\circ }$ = 3 × 40${}^{\circ }$ - 10${}^{\circ }$ = 110${}^{\circ }$