Math / Geometry

Question2 3 4 5 6 7 8 9 10
In the diagram of circle $P, m \angle X Y Z$ is $72^{\circ}$ . What is the value of $x$ ? $108^{\circ}$ $144^{\circ}$ $216^{\circ}$ $252^{\circ}$

Studdy Solution

STEP 1

1. The circle is centered at point $P$ .
2. Points $X$ , $Y$ , and $Z$ are on the circumference of the circle.
3. $\angle XYZ$ is an inscribed angle that subtends arc $XZ$ .
4. The measure of $\angle XYZ$ is $72^\circ$ .
5. The central angle subtending the same arc $XZ$ is $x^\circ$ .

STEP 2

1. Recall the relationship between an inscribed angle and its corresponding central angle.
2. Use the relationship to find $x$ .

STEP 3

Recall the relationship between an inscribed angle and its corresponding central angle:
The measure of an inscribed angle is half the measure of its corresponding central angle.
$m \angle XYZ = \frac{1}{2} \times m \angle XPZ$

STEP 4

Use the relationship to find $x$ :
Given $m \angle XYZ = 72^\circ$ , we have:
$72^\circ = \frac{1}{2} \times x$
Solve for $x$ :
$x = 2 \times 72^\circ$ $x = 144^\circ$
The value of $x$ is:
$\boxed{144^\circ}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms