pinklands08
Answered

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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

Sagot :

goodLizard

Answer:

Part A: D. [tex]3x+x=180[/tex]

Part B: Smaller angle [tex]=45^{\circ}[/tex], larger angle [tex]=135^{\circ}[/tex]

Explanation:

The term supplementary is used when the sum of two angles add to [tex]180^{\circ}[/tex].

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:

[tex]3x+x=180[/tex]

Part B:

To find the measure of each angle, we can first find the measure of the smaller angle [tex]x[/tex]:

[tex]3x+x=180[/tex]

[tex]4x=180[/tex]

[tex]x=45^{\circ}[/tex]

[tex]\therefore[/tex] The smaller angle is [tex]45^{\circ}[/tex]

Since the measure of the larger angle is [tex]3[/tex] times the measure of the smaller angle:

Larger angle [tex]=3x[/tex]

[tex]=3(45)[/tex]

[tex]=135^{\circ}[/tex]

[tex]\therefore[/tex] The measure of the larger angle is [tex]135^{\circ}[/tex]

Hope this helps :)

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