Question

if a point c is inside ∠avb, then ____ + m∠cvb = m∠avb,
m∠avb = 62°
options:
a. m∠avb
b. m∠bvc
c. m∠avc
d. m∠cvb

Explanation:

When a point \( C \) is inside \( \angle AVB \), the angle - addition postulate states that the measure of the larger angle \( \angle AVB \) is equal to the sum of the measures of the two smaller angles formed by a ray (in this case, ray \( VC \)) that splits the larger angle. That is, \( m\angle AVC + m\angle CVB=m\angle AVB \).

For option A, \( m\angle AVB + m\angle CVB
eq m\angle AVB \) (it would be larger than \( m\angle AVB \)). For option B, \( \angle DVC \) is not related to the angles forming \( \angle AVB \) as per the diagram and the angle - addition context here. For option D, \( m\angle CVB + m\angle CVB = 2m\angle CVB
eq m\angle AVB \) (unless \( m\angle AVC=m\angle CVB \), which is not given). So the correct answer is C.

Answer:

C. \( m\angle AVC \)