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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 1: Q. 29 WE (page 22)

$\overset{\leftrightarrow}{A L}$ bisects $∠ K A T$ . Find the value of $x$ .
$m ∠ 3 = 6 x$ , $m ∠ K A T = 90 - x$

Short Answer

Expert verified

The value of $x$ is $18^{o}$ .

Step by step solution

01

- Line bisector and straight angle

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

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

02

- Observe the figure

The given figure is

From the figure, since $S A T$ is a straight line, therefore,

$m ∠ 3 + m ∠ K A T = 180^{°}$

03

- Calculate x.

In order to calculate the value of $x$ , substitute $6 x$ for $m ∠ 3$ and $90 - x$ for $m ∠ K A T$ into the equation $m ∠ 3 + m ∠ K A T = 180^{°}$ and simplify.

$\begin{matrix} 6 x + 90^{°} - x = 180^{°} \\ 5 x + 90^{°} = 180^{°} \end{matrix}$

Subtract $90^{°}$ from both sides.

$\begin{matrix} 5 x + 90^{°} - 90^{°} = 180^{°} - 90^{°} \\ 5 x = 90^{°} \\ x = \frac{90^{°}}{5} \\ x = 18^{°} \end{matrix}$

Therefore, $x = 18^{°}$ .

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Most popular questions from this chapter

Suppose you were asked to find a point 5 cm from P, 5 cm from F, and 5 cm from T. Is there such a point?

For the following figure, name the midpoint of $P T$ .

Sketch and label the figures described. Use dashes for hidden parts.

Point P is not in plane N. Three lines through point P intersect N in points A, B, and C.

Name a fourth point that is in the same plane as the given points.

E, F, H

The plane that contains the top of the box can be called plane ABCD.

Are there any points besides C and G?

See all solutions

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