Find the measure of angle Z.

We are given a figure with a triangle with two known angles and one unknown angle. That unknown angle further extends to form a straight line and we are to find that exterior angle z.

We know that the sum of all three angles of a triangle is 180°. So the third unknown angle of the given triangle will be = 180 - (45 + 72) = 63°.

We also know that angles on one side of a straight line always add to 180°.

Therefore, angle z = 180 - 63 = 117°.

lhabdulsamirahmed lhabdulsamirahmed · Answer 2 · 2022-04-20T16:16:47+02:00

The value of angle z is 114°

Data;

72°
42°
z = ?

Angle in a Triangle

To find the missing angle z, we can find the sum of angles in the triangle which will enable us find the third missing angle x

[tex]x + 72 + 42 = 180 \\x = 180 - 114\\x = 66^0[/tex]

The reason behind this is that the sum of angles in a triangle is equal to 180°

z + x = 180°

Reason: Sum of angles on a straight line is equal to 180°

[tex]66 + z = 180 \\z = 180 - 66\\z = 114^0[/tex]

The value of angle z is 114°

Learn more on sum of angle in a triangle here;

https://brainly.com/question/11966001