Question

If the angles $(2a-10{)}^{\circ }$ and $(a-11{)}^{\circ }$ are complementary, then find the value of a.

• A. ${37}^{\circ }$
• B. ${27}^{\circ }$
• C. ${17}^{\circ }$
• D. $7^{\circ }$

Answer 1

The correct option is A

${37}^{\circ }$

Given, the angles $(2a-10{)}^{\circ }$ and $(a-11{)}^{\circ }$ are complementary angles.
$\therefore (2a-10{)}^{\circ }+(a-11{)}^{\circ }={90}^{\circ }$

$\Rightarrow (3a-21{)}^{\circ }={90}^{\circ }$

$\Rightarrow 3a={111}^{\circ }$
$\Rightarrow a={37}^{\circ }$