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If Cand Dare complementary, find the value of y, mCand mD.

mC=3y+5,mD=2y

Short Answer

Expert verified

The value of y is 17.

The measures of the angles C and D are 56° and 34°.

Step by step solution

01

Step 1. Definition of complementary angles.

The complementary angles are the angles whose sum is 90°.

02

Step 2. Write the relation between the angles C and D.

As the angles C andD are complementary, therefore, the sum of the angles C andD is 90°.

Therefore, the relation between the angles C and D is:mC+mD=90°

03

Step 3. Find the value of y.

Find the value of y by using the relation mC+mD=90°.

Therefore,

mC+mD=90°3y+5+2y=905y+5=905y=90-55y=85y=855y=17

Therefore, the value of y is 17.

04

Step 4. Find the measure of the angle C.

Substitute 17 for y into mC=3y+5 to find the measure of the angle C.

Therefore,

mC=3y+5=3×17+5=51+5=56

Therefore, the measure of angleC is 56°.

05

Step 5. Find the measure of the angle D.

Substitute 17 fory intomD=2y to find the measure of the angle D.

Therefore,

mD=2y=2×17=34

Therefore, the measure of the angle D is 34°.

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