Question

Draw a diagram that satisfies the conditions stated. If the conditions cannot be satisfied, write not possible.

The measure of a supplement of an angle is 35 more than twice the complement of the angle. Find the measure of the angle, its supplement, and its complement.

Short answer

The angle is 35°, the supplementary angle is 145° and the complementary angle is 55°.

The diagram is:

Step-by-step solution

Step 1. Define supplementary and complementary angles.

The sum of two angles whose sum is 180° are called supplementary angles and complementary angles are the two angles whose sum is 90°.

Step 2. Show the calculation.

Given that:The measure of the supplement of an angle is35more than the twice of a complement.

Let the angle be x.

Supplement of x is $180-x$.

Complement of x is $90-x$.

Then from the data:

$\begin{array}{c}180-x=35+2\left(90-x\right)\\ 180-x=35+180-2x\\ x=35\end{array}$

Therefore, $x=35°$.

Step 3. State the conclusion.

As $x=35°$,

Then,

$\begin{array}{c}\text{Supplementaryangle}={180}^{\circ }-x\\ ={180}^{\circ }-{35}^{\circ }\\ ={145}^{\circ }\end{array}$

And

$\begin{array}{c}\text{Complementaryangle}={90}^{\circ }-x\\ ={90}^{\circ }-{35}^{\circ }\\ ={55}^{\circ }\end{array}$

Therefore,

Angle =35°,

Supplementary angle=145°and

Complementary angle=55°.

The diagram is: