Chapter 3: Q9. (page 112)

Find the measures of the numbered angles.
XYZis regular.

Short Answer

Expert verified

The measures of $∠ 1, ∠ 2$ and $∠ 3$ is $60 °, 60 °$ and $120 °$ respectively.

Step by step solution

Step 1. Description of step.

A regular triangle is a triangle in which all the three sides are congruent and all interior angles are congruent.

Step 2. Description of step.

For triangle XYZ, a measure of each angle is

$\begin{array}{l} = \frac{180}{3} \\ = 60 ° \end{array}$

Therefore, $m ∠ X Z Y = m ∠ 1 = m ∠ 2 = 60 °$ .

Step 2. Apply the exterior angle theorem.

The measure of an exterior angle is equal to the sum of measure of remote interior angles.

In $Δ X Y Z$ , $∠ 1, ∠ 2$ are remote interior angles and $∠ 3$ is an exterior angle than by exterior angle theorem,

$\begin{matrix} m ∠ 3 = m ∠ 1 + m ∠ 2 \\ = 60 + 60 \\ = 120 ° \end{matrix}$

Therefore, the measures of $∠ 1, ∠ 2$ and $∠ 3$ is $60 °, 60 °$ and $120 °$ respectively.

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Find the measures of the numbered angles.
XYZis regular.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 2. Apply the exterior angle theorem.

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Find the measures of the numbered angles.XYZis regular.

Short Answer

Step by step solution

Step 1. Description of step.

Step 2. Description of step.

Step 2. Apply the exterior angle theorem.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Find the measures of the numbered angles.
XYZis regular.