Question

The measure of the supplement of $\angle A$ is $40$ degrees larger than twice the measure of the complement of angle $A$. What is the sum of the measures of the supplement and complement of angle $A$?

• A. ${190}^{\circ }$
• B. ${120}^{\circ }$
• C. ${170}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is A ${190}^{\circ }$

Let angle $A\text{be}{x}^{\circ }.$

The supplement of angle $A=(180-x{)}^{\circ }$

The complement of angle $A=(90-x{)}^{\circ }$

From the condition, the supplement of angle $A$ is ${40}^{\circ }$ more than twice the measure of complement of angle $A$.
$180-x=2(90-x)+40$
$180-x=180-2x+40$

$2x-x=180-180+40$
$x=40$

Supplement of $A=180-x=180-40={140}^{\circ }$

Complement of $A=90-x=90-40={50}^{\circ }$

The sum of supplement and complement of angle $A=140+50={190}^{\circ }$