Question

Two angles are supplementary and the larger is 40 degree less than the three times the smaller. find the smaller angle .​

Answer 1

Answer :-

• let the smaller angle be x

then, according to the question

• larger angle = 3x - x

and we know that,

• sum of supplementary angles is equal to 180°

$\bold{: \implies x + 3x - 40 \degree= 180 \degree} \\ \\ \bold{: \implies 4x - 40 \degree = 180 \degree} \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 4x = 180 \degree + 40 \degree} \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 4x = 220 \degree } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = \cancel\frac{220 \degree}{4} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 55 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, value of smaller angle is 55°