Question

Two angles of a quadrilateral measure 215° and 70°. The other two angles are in a ratio of 2:13. What are the measures of those two angles?

Answer 1

The sum of the interior angles of a quadrilateral is 360°.

The ratio of 2 angles is 2 : 13. Take them as 2x° & 13x°.

Now, solve for x.

$\mathfrak{215+70+2x+13x=360}$

$\mathfrak{285+15x=360}$

$\mathfrak{15x=360-285}$

$\mathfrak{15x=75}$

$\mathfrak{x=\dfrac{75}{15}}$

$\underline{\mathfrak{x=5}}$

So,

2x = 2(5) = $\boxed{\mathfrak{10^{\circ}}}$

13x = 13(5) = $\boxed{\mathfrak{65^{\circ}}}$

$\mathbb{MIREU}$