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NeX [460]
2 years ago
9

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

Mathematics
1 answer:
Ugo [173]2 years ago
4 0

Answer:

∠ CPM  = 135°

Step-by-step explanation:

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

∠ ABC = \frac{180-40}{2} = \frac{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°

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