Question

In a triangle ABC, $\angle$A - $\angle$B = ${30}^{\circ }$ and $\angle$A - $\angle$C = ${42}^{\circ }$; find angle A.

• A. A = ${84}^{\circ }$
• B. A = ${64}^{\circ }$
• C. A = ${95}^{\circ }$
• D. A = ${92}^{\circ }$

Answer 1

The correct option is A A = ${84}^{\circ }$

$\angle A-\angle B=30$ (Eq. I)
$\angle A-\angle C=42$ (Eq. II)
$\angle A+\angle B+\angle C=180$ (Eq. III) (Sum of angles of triangle)
Add all the three equations,
$3\angle A=30+42+180$
$3\angle A=252$
$\angle A={84}^{\circ }$