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Chapter 2: Q26. (page 53)

If 鈭�Cand 鈭�Dare complementary, find the value of y, m鈭�Cand m鈭�D.

m鈭�C=3y+5,m鈭�D=2y

Short Answer

Expert verified

The value of y is 17.

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

Step by step solution

01

Step 1. Definition of complementary angles.

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

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掳.

Therefore, the relation between the angles C and D is:m鈭�C+m鈭�D=90掳

03

Step 3. Find the value of y.

Find the value of y by using the relation m鈭�C+m鈭�D=90掳.

Therefore,

m鈭�C+m鈭�D=90掳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 m鈭�C=3y+5 to find the measure of the angle C.

Therefore,

m鈭�C=3y+5=3脳17+5=51+5=56

Therefore, the measure of angleC is 56掳.

05

Step 5. Find the measure of the angle D.

Substitute 17 fory intom鈭�D=2y to find the measure of the angle D.

Therefore,

m鈭�D=2y=2脳17=34

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

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