∠B= 100 ∠A+∠C=80

Because am = anCN=CP

So ∠ CNP+∠ ANM = (360-80) ÷ 2 =140.

∠MNP= 180 - 140 =40

2.

Extend AE to BC at point F.

∠AEC =∠FEC = 90 CE∠ABC so∠CFA =∠ 1。

German BC, so ∠AFB=∠2.

3.

This problem also needs auxiliary lines.

Do DG⊥BC and you can see △ Abd △ BDG.

∠A=90 AB=AC

So ad = DG = GC(≈C = 45)

So AB+AD=BG+GC

AB+AD=BC

4.

Let BD = CD = X.

At △ABD

three