Question

Given that ⊙M≅⊙N and XZ◠≅BC◠, find m∠XMZ.

Answer 1

∠ XMZ = 74°

Explanation:

Since the corresponding arcs on the 2 circles are congruent , then the central angles are congruent, that is

6x - 88 = 3x - 7 ( subtract 3x from both sides )

3x - 88 = - 7 ( add 88 to both sides )

3x = 81 ( divide both sides by 3 )

x = 27

Then

∠ XMZ = 3x - 7 = 3(27) - 7 = 81 - 7 = 74°