Two angles are complementary.If one angle is 30 degrees more than thrice the oth...

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October 2022 1 6 Report

Two angles are complementary.If one angle is 30 degrees more than thrice the other, what are the degree measure of the two angles???

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RobbieRavenclaw

Verified answer

Answer:

The measurement of the first angle is 15°, and the measurement of the second angle is 75°.

Step-by-step explanation:

If they are complementary, then their sum would be 90°.

Given:

$m\angle1=x$
$m\angle2=3x+30^{\circ}$

Find:

$m\angle1=?$

$m\angle1=?$

Formula:

$m\angle1+m\angle2=90^{\circ}$

Solution:

$m\angle1+m\angle2=90^{\circ}\\x+3x+30^{\circ}=90^{\circ}\\4x=90^{\circ}-30^{\circ}\\4x=60^{\circ}\\\frac{4x}{4}=\frac{60^{\circ}}{4}\\\boldsymbol{x=15^{\circ}}$

$m\angle1=x\\\boxed{\boldsymbol{m\angle1=15^{\circ}}}$

$m\angle2=3x+30^{\circ}\\m\angle2=3(15^{\circ})+30^{\circ}\\m\angle2=45^{\circ}+30^{\circ}\\\boxed{\boldsymbol{m\angle2=75^{\circ}}}$

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Verified answer

The measurement of the first angle is 15°, and the measurement of the second angle is 75°.

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