Question

Q2. The interior angles of a quadrilateral are (2x + 15)°, (3x + 75)° and (3x – 25)°. i. Find the value of x. ii. Find the smallest interior angle of the quadrilateral. iii. Find the smallest exterior angle of the quadrilateral.

Answer 1

x =30°

Step-by-step explanation:

We know sum of the interior angles of a quadrilateral is 360^{\circ}

therefore we can write

(2x+15)+(2x-5)+(3x+75)+(3x-25)=360^{\circ}

so

\Rightarrow 10x+60=360

\Rightarrow 10x=300

\Rightarrow x=30^{\circ}

So smallest interior angle is (2x-5)^{\circ}=(60-5)=55^{\circ}

Largest interior angle =3x+75=90+75=165^{\circ}