Question

The measure of the supplement of an angle is 46 more than 3 times the compliment of the angle. Find the angle.

Answer 1

Answer: 68 degrees

Explanation:

Let the measure of the angle be x.

The supplement of the angle is 180 - x as supplementary angles add up to 180 degrees.

The complement of the angle is 90 - x as complementary angles add up to 90 degrees.

We can set up an equation.

180 - x = 46 + 3*(90-x)

180 - x = 46 + 270 - 3x

Combine like terms:

2x = 136

Divide both sides by 2:

x = 68

Answer 2

What are supplementary and complementary angles?

• Supplementary angles are angles whose measure adds up to 180°
• Complementary angles are angles whose measure adds up to 90°

1. First, let's assign a variable to the unknown angle: x
2. Next, set up an equation that represents the information you were given:

The supplement of an angle (180 - x) is [=] 46 more than 3 times the complement (90-x):

180 - x = 3 (90 - x) +46

Now, solve for x:

180 - x = 3 (90 - x) +46

180 - x = 270 - 3x +46

180 - x = 316 -3x

-x = 136 -3x

2x = 136

x = 68

The angle is 68°