A and a' are vertical angles, therefore a' = a

We know: The sum of the measures of triangle is always 180°.

Therefore: a' + b + d = 180° → d = 180° - a - b.

d and c are adjacent angles, therefore d + c = 180°

substitute

180° - a - b+ c = 180° |-180°
-a - b + c = 0 |+a |+b
c = a + b

4 0

3 years ago

Which circle has a central angle that measures 40°?

Varvara68 [4.7K]

Answer:

Option B.

Step-by-step explanation:

We need to find the circle that has a central angle that measures 40°.

In all options, the center of circle is U. It means central angle must be on center, i.e., U.

In option A,the angle VXZ is at point X which is not the center. So, angle VXZ is not a central angle.

In option B,the angle VUZ is at point U which is the center. So, angle VUZ is a central angle with measure 40°.

In option C,the angle XZV is at point Z which is not the center. So, angle XZV is not a central angle.

In option D,the angle VXZ is at point X which is not the center. So, angle VXZ is not a central angle.

Therefore, the correct option is B.

8 0

3 years ago