Question

AC = BC, <ACB = 40°, <AMN = 25° <CPM = ?​

Answer 1

∠ CPM = 135°

Explanation:

given AC = BC , then Δ ABC is isosceles with base angles congruent , then

∠ ABC =
`(180-40)/(2)` =
`(140)/(2)` = 70°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, then

∠ AMN + ∠ BPM = ∠ ABC , that is

25° + ∠ BPM = 70° ( subtract 25° from both sides )

∠ BPM = 45°

∠ CPM and ∠ BPM are adjacent angles on a straight line and sum to 180°

∠ CPM + 45° = 180° ( subtract 45° from both sides )

∠ CPM = 135°