## In ΔABC, m∠ABC = 40°, BL is the angle bisector of ∠B with point L∈ AC . Point M ∈ AB so that LM ⊥ AB and N ∈ BC so that LN ⊥ BC

Question

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## Answers ( No )

It can help to draw a diagram.

∆LBM ≅ ∆LBN by the hypotenuse-angle (HA) theorem of congruence of right trianges. Then LM ≅ LN and BM ≅ BN by CPCTC. Quadrliateral BMLN is a kite, so diagonal MN ⊥ BL.

Of course, angles BLN and BLM are the complements of the halves of bisected angle B, so are both 70°. And angles LMN and LNM are the complements of those, so are both 20°.

∆MNL is an isosceles triangle with base angles of 20° and an apex angle of 140°.