1 Answer

Vinayak Kolagi · Answer 1 · 2024-09-03T03:11:41+0000

Here we go ~

As we know, a complete cycle/angle measures 360

And the exterior one there is 110°, let the interior angle be y ~

$\qquad\displaystyle \tt \rightarrow \: y + 110 \degree = 360 \degree$

$\qquad\displaystyle \tt \rightarrow \: y = 360 \degree - 110 \degree$

$\qquad\displaystyle \tt \rightarrow \: y = 250 \degree$

Also, we know sum of all interior angles of a qadrilateral is 360° as well ~

So, lets add 'em ~

$\qquad\displaystyle \tt \rightarrow \: x + x + 50 \degree + 250 \degree = 360 \degree$

$\qquad\displaystyle \tt \rightarrow \: 2x +300 \degree = 360 \degree$

$\qquad\displaystyle \tt \rightarrow \: 2x = 360 \degree - 300 \degree$

$\qquad\displaystyle \tt \rightarrow \: 2x = 60 \degree$

$\qquad\displaystyle \tt \rightarrow \: x = 60 \degree / 2$

$\qquad\displaystyle \tt \rightarrow \: x = 30 \degree$

Hence~ the value of x is 30°