Question

If lines $l$ || m and $\angle$a : $\angle$ b = 3 : 2, $\angle$Q = 90${}^o$ and $\angle$b + $\angle$c = 100${}^o$, then find $\angle$P from given figure.

• A. 26${}^o$
• B. 32${}^o$
• C. 12${}^o$
• D. 62${}^o$

Answer 1

The correct option is A 26${}^o$

In triangle ABQ,
a : b = 3 : 2, Q = 90
Let's assume a=3x and b=2x
So, 3x+2x=90
$x=18$
a=3x=18*3=54
b=2x=18*2=36
lines l || m and ab is crossing the parallel line.
So, $a+p+b+c=180$
$a+p+100=180$
$54+p=80$
$p=26$
Answer (A) $26$