Question

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

• A. 70 and 110
• B. 60 and 120
• C. 50 and 130
• D. 40 and 140

Answer 1

The correct option is A

70 and 110

The angles are a linear pairs, hence 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${}^{\circ }$