Chapter 12: Q6. (page 688)

In Example 3, suppose that $m ∠ 1 = 135 °$ . Find $m ∠ 2$ , $m ∠ 3$ , and $m ∠ 4$ .

Short Answer

Expert verified

The measures of the other three angles $m ∠ 2, m ∠ 3,$ and $m ∠ 4$ are $45 {}^{\circ}, 135 {}^{\circ},$ and $45 °$ respectively.

Step by step solution

Step 1. Given Information.

$m ∠ 1 = 135 °$ . The figure is shown below.

Step 2. Concept used.

When two lines intersect, the angles opposite each other are called ‘vertical angles’ and they have the same measure.
If two adjacent angles form a straight angle, then the two angles are supplementary angles and the sum of their measures is $180 °$ .

Step 3. Calculation.

In the given figure, $∠ 1$ and $∠ 3$ are vertical angles. So, they should have the same measure. Therefore,

$m ∠ 3 = m ∠ 1 = 135 °$

Also, in the given figure, $∠ 1$ and $∠ 2$ are supplementary angles as they are adjacent and form a straight angle. So, the sum of their measures should be $180 °$ .

Therefore,

$\begin{matrix} m ∠ 1 + m ∠ 2 = 180 ° \\ m ∠ 2 = 180 ° - m ∠ 1 \\ = 180 ° - 135 ° \\ = 45 ° \end{matrix}$

Similarly, $∠ 1$ and $∠ 4$ are supplementary angles.

Therefore,

$\begin{matrix} m ∠ 1 + m ∠ 4 = 180 ° \\ m ∠ 4 = 180 ° - m ∠ 1 \\ = 180 ° - 135 ° \\ = 45 ° \end{matrix}$

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In Example 3, suppose that $m ∠ 1 = 135 °$ . Find $m ∠ 2$ , $m ∠ 3$ , and $m ∠ 4$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

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In Example 3, suppose that m∠1=135°. Find m∠2, m∠3, and m∠4.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Calculus

Applied Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

In Example 3, suppose that $m ∠ 1 = 135 °$ . Find $m ∠ 2$ , $m ∠ 3$ , and $m ∠ 4$ .