Chapter 1: Q. 32 WE (page 22)

$\overset{\leftrightarrow}{A L}$ bisects $∠ K A T$ . Find the value of $x$ .
$m ∠ 1 = x$ , $m ∠ 3 = 4 x$

Short Answer

Expert verified

The value of $x$ is $30^{o}$ .

Step by step solution

- Line bisector and straight angle

If a line bisects angles, it divides it into two equal parts.

Measure of straight angle is $180^{o}$ .

- Observe the figure

The given figure is

From the figure, since $\overset{\leftrightarrow}{A L}$ bisects $∠ K A T$ , therefore, $m ∠ 1 = m ∠ 2 = x$ .

Also, $∠ S A T$ is a straight angel therefore.

$m ∠ 1 + m ∠ 2 + m ∠ 3 = 180^{o}$

- Calculate x.

In order to calculate the value of $x$ , substitute $x$ for $m ∠ 1$ , $x$ for $m ∠ 2$ , $4 x$ for $m ∠ 3$ into the equation $m ∠ 1 + m ∠ 2 + m ∠ 3 = 180^{o}$ and simplify.

$\begin{matrix} x + x + 4 x = 180^{o} \\ 6 x = 180^{o} \\ \frac{6 x}{6} = \frac{180^{o}}{6} \\ x = 30^{o} \end{matrix}$

Therefore, $x = 30^{o}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$\overset{\leftrightarrow}{A L}$ bisects $∠ K A T$ . Find the value of $x$ .
$m ∠ 1 = x$ , $m ∠ 3 = 4 x$

Short Answer

Step by step solution

- Line bisector and straight angle

- Observe the figure

- Calculate x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

AL↔bisects ∠KAT. Find the value of x.m∠1=x,m∠3=4x

Short Answer

Step by step solution

- Line bisector and straight angle

- Observe the figure

- Calculate x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

$\overset{\leftrightarrow}{A L}$ bisects $∠ K A T$ . Find the value of $x$ .
$m ∠ 1 = x$ , $m ∠ 3 = 4 x$