Question

This question has two parts. Use the information to answer Part A and Part B.

Two angles are supplementary. The measure of one angle is 3 times the measure of the other angle.
Part A
Which equation can be used to find x, the measure of the smaller angle in degrees?
A. 3x - x=90
o
B. 3x + x = 90
o
C. 3x - x = 180
D. 3x + x = 180
Part B
What is the measure of each angle? Enter the answers in the boxes.
The smaller angle measures
and the larger angle measures

Answer 1

Part A: D.
`3x+x=180`

Part B: Smaller angle
`=45^(\circ)`, larger angle
`=135^(\circ)`

Step-by-step explanation:

The term supplementary is used when the sum of two angles add to
`180^(\circ)`.

Part A:

From the information given that the "angles are supplementary" and the "measure of one angle is 3 times the measure of the other", the equation to find for x can be written as:

`3x+x=180`

Part B:

To find the measure of each angle, we can first find the measure of the smaller angle
`x`:

`3x+x=180`

`4x=180`

`x=45^(\circ)`

`\therefore` The smaller angle is
`45^(\circ)`

Since the measure of the larger angle is
`3` times the measure of the smaller angle:

Larger angle
`=3x`

`=3(45)`

`=135^(\circ)`

`\therefore` The measure of the larger angle is
`135^(\circ)`

Hope this helps :)