Chapter 2: Q27 (page 53)

If $∠ C$ and $∠ D$ are complementary, find the value of y, $m ∠ C$ and $m ∠ D$ .
$m ∠ C = y - 8$ , $m ∠ D = 3 y + 2$

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

Step 1. Definition of complementary angles.

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

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: $m ∠ C + m ∠ D = 90 °$

Step 3. Find the value of y.

Find the value of y by using the relation $m ∠ C + m ∠ D = 90 °$ .

Therefore,

$m ∠ C + m ∠ D = 90 ° y - 8 + 3 y + 2 = 90 4 y - 6 = 90 4 y = 90 + 6 4 y = 96 y = \frac{96}{4} y = 24$

Therefore, the value of y is 24.

Step 4. Find the measure of the angle C.

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

Therefore,

$m ∠ C = y - 8 \begin{matrix} = 24 - 8 \\ = 16 \end{matrix}$

Therefore, the measure of angle C is 16°.

Step 5. Find the measure of the angle D.

Substitute 24 foryinto $m ∠ D = 3 y + 2$ to find the measure of the angle D.

Therefore,

$m ∠ D = 3 y + 2 = 3 \times 24 + 2 = 72 + 2 = 74$

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

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If $∠ C$ and $∠ D$ are complementary, find the value of y, $m ∠ C$ and $m ∠ D$ .
$m ∠ C = y - 8$ , $m ∠ D = 3 y + 2$

Short Answer

Step by step solution

Step 1. Definition of complementary angles.

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

Step 3. Find the value of y.

Step 4. Find the measure of the angle C.

Step 5. Find the measure of the angle D.

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If ∠Cand ∠Dare complementary, find the value of y, m∠Cand m∠D.m∠C=y-8,m∠D=3y+2

Short Answer

Step by step solution

Step 1. Definition of complementary angles.

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

Step 3. Find the value of y.

Step 4. Find the measure of the angle C.

Step 5. Find the measure of the angle D.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Pure Maths

Mechanics Maths

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Logic and Functions

Study anywhere. Anytime. Across all devices.

If $∠ C$ and $∠ D$ are complementary, find the value of y, $m ∠ C$ and $m ∠ D$ .
$m ∠ C = y - 8$ , $m ∠ D = 3 y + 2$