Question

Which expression gives the measure of ZXYZ?

110"
D
42°
Z
A. 110° -42°
B. 110° +42°
O C. (110° +42°)
OD. (110° -42°)

Answer 1

The measure of angle XYZ in a circle, divided by lines UZ and WX, is found by subtracting the given angle UYW from 180. The correct expression is 1/2(110 - 42), corresponding to option a.

The sum of the angles in a triangle is always 180 degrees. In the given circle, angles XYZ and UYW form a linear pair, meaning they are supplementary (their sum is 180 degrees). Therefore:

`\[ \text{angle XYZ} = 180 - \text{angle UYW} \]`

Substitute the given values:

`\[ \text{angle XYZ} = 180 - 110 \]`

`\[ \text{angle XYZ} = 70 \]`

So, the correct expression for the measure of angle XYZ is:

`\[ \text{1/2} * (110 - 42) \]`

This corresponds to option a.
`\((1)/(2)(110 - 42)\).`