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

mC=y-8,mD=3y+2

Short Answer

Expert verified

The value of y is 24.

The measures of the angles C and D are 16° and 74°.

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°y-8+3y+2=904y-6=904y=90+64y=96y=964y=24

Therefore, the value of y is 24.

04

Step 4. Find the measure of the angle C.

Substitute 24 for y into mC=y-8 to find the measure of the angle C.

Therefore,

mC=y-8=24-8=16

Therefore, the measure of angle C is 16°.

05

Step 5. Find the measure of the angle D.

Substitute 24 foryintomD=3y+2 to find the measure of the angle D.

Therefore,

mD=3y+2=3×24+2=72+2=74

Therefore, the measure of the angle D is 74°.

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