Question

In the given figure PQ is perpendicular to AB, AQ =QB, angle PAC =42° angle c =68° Find angle ABC​

Answer 1

★ Brainly Teacher ★

Answer:

M is the midpoint of PQ

M is the midpoint of AB

Step-by-step explanation:

Given:

PA = QB ............(1)

In ΔAPM and ΔBQM,

∠M=∠M (common)

∠A=∠B=90

∠P=∠Q

ΔAPM and ΔBQM are equiangular

By AAA similarity,

ΔAPM and ΔBQM are similar.

Their corresponding sides are proportional.

\frac{AP}{BQ}=\frac{PM}{QM}=\frac{AM}{BM}\\\\using\:(1)\\\\1=\frac{PM}{QM}=\frac{AM}{BM}\\\\\frac{PM}{QM}=1\\\\PM=QM

PA = QB

PA/QB = 1

AM/ BM = MP/MQ = 1

This implies, M is the midpoint of PQ

\frac{AM}{BM}=1\\\\AM=BM

This implies, M is the midpoint of AB...

that's solved

thanks