Chapter 12: Q35. (page 691)

Let $∠ 1$ and $∠ 2$ be complementary angles, and let $∠ 2$ and $∠ 3$ be supplementary angles. If $m ∠ 1 = x °$ and $m ∠ 2 = 2 x °$ , find x. Then find $m ∠ 1$ , $m ∠ 2$ , and $m ∠ 3$ .

Short Answer

Expert verified

The value of x is $30 °$ . $m ∠ 1 = 30 {}^{\circ}, m ∠ 2 = 60 {}^{\circ},$ and $m ∠ 3 = 120 °$

Step by step solution

Step 1. Given Information.

$m ∠ 2 = 2 x {}^{\circ}{and} m ∠ 1 = x °$

Step 2. Calculation.

Since, complementary angles are those whose sum of the angles is $90 °$ . That is,

m ∠ 1 + m ∠ 2 = 90 °

…… (1)

Find x using equation (1).

$\begin{matrix} x ° + 2 x ° = 90 ° \\ 3 x ° = 90 ° \\ x = \frac{90 °}{3 °} \\ x = 30 ° \end{matrix}$

Thus, the value of x is $30 °$ .

Therefore, the angle measures are $30 °$ , $60 °$ .

Also, supplementaryangles are those whose sum of the angles is $180 °$ . That is,

$m ∠ 2 + m ∠ 3 = 180 °$ ……. (2)

Find x using equation (2).

$m ∠ 2 + m ∠ 3 = 180 °$

Since, $m ∠ 2 = 60 °$

Therefore, the equation (2) becomes,

$\begin{matrix} 60 ° + m ∠ 3 = 180 ° \\ m ∠ 3 = 180 ° - 60 ° \\ m ∠ 3 = 120 ° \end{matrix}$

Therefore, $m ∠ 3 = 120 °$ .

Step 3. Conclusion.

The angles are $m ∠ 1 = 30 {}^{\circ}, m ∠ 2 = 60 {}^{\circ},$ and $m ∠ 3 = 120 °$ .

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Let $∠ 1$ and $∠ 2$ be complementary angles, and let $∠ 2$ and $∠ 3$ be supplementary angles. If $m ∠ 1 = x °$ and $m ∠ 2 = 2 x °$ , find x. Then find $m ∠ 1$ , $m ∠ 2$ , and $m ∠ 3$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Let ∠1and ∠2be complementary angles, and let ∠2and ∠3be supplementary angles. If m∠1=x° and m∠2=2x°, find x. Then find m∠1, m∠2, and m∠3.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

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Let $∠ 1$ and $∠ 2$ be complementary angles, and let $∠ 2$ and $∠ 3$ be supplementary angles. If $m ∠ 1 = x °$ and $m ∠ 2 = 2 x °$ , find x. Then find $m ∠ 1$ , $m ∠ 2$ , and $m ∠ 3$ .