Question

Use the information given in the following figure to find :

(i) x

(ii) $\angle Band\angle C$

Answer 1

$\because \angle A={90}^o\angle B=(2x+4^o)\angle C=(3x-5^o)\angle D=(8x-{15}^o)\angle A+\angle B+\angle C+\angle D={360}^o{90}^o+(2x+4^o)+(3x-5^o)+(8x-{15}^o)={360}^o{90}^o+2x+4^o+3x-5^o+8x-{15}^o={360}^o\Rightarrow {74}^o+13x={360}^o\Rightarrow 13x={360}^o-{74}^o\Rightarrow 13x={286}^o\Rightarrow x={22}^o\because \angle B=2x+4=2\times {22}^o+4={48}^o\angle C=3x-5=3\times {22}^o-5={61}^{o}Hence\left(i\right){22}^o\left(ii\right)\angle B={48}^o,\angle C={61}^o$.