Question

Angles around a point
Grade 8

Answer 1

x=45, y=45, z= 131

Explanation:

x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.

Now that there are 2 right angles, that makes up 180. 180+49=229

A full rotation is 360, so you subtract that. 360-229=131
z=131.

Answer 2

• x = 41°
• y = 49°
• z = 131°

Explanation:

The relevant relations are ...

• a straight angle measures 180°
• a right angle measures 90°
• vertical angles have the same measure

__

The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.

y = 49°

The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.

x + y = 90°

x + 49° = 90°

x = 41° . . . . . . . . . subtract 49°

The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")

49° +z = 180°

z = 131° . . . . . . . subtract 49°

The measures of the marked angles are ...

x = 41°

y = 49°

z = 131°