Question

Please help me solve these questions

Answer 1

According to the question

$ab || cd$
$\\ \\ \\ l \: is \: transversal \: line$



angle A + B = 180 (corresponding angles)


angle A = CAP + PAB or

$angle \: \: \: \: c \: a \: p = \frac{a}{2}$
(angle bisector)

$angle \: \: \: \: p \: a \: b \: = \frac{c}{2}$
(angle bisector)


therefore

$a + b \: = 180 \\ \\ \frac{a}{2 } + \frac{b}{2} = \frac{180}{2} \\ \\ or \: angle \: \: \: pac \: + pca = 90$

in triangle apc



pac + pca + apc = 180 (sum of angles of

triangle)



pac +pca = 90( from above)



therefore


90 + APC = 180


APC = 180 - 90



APC = 90°



hence proved







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