Question

find the measure of angle X in the following figure. 50° 90° 110°​

Answer 1

Answer:

$\sf\tt\large{\green {\underline {\underline{⚘\;Given. :}}}}$

• First angle is 50°
• Second angle is 90°
• Third angle is 110°

To Find:-

• Fourth Angle

$\sf \pink{Solution - }$

$\sf \: = 360 {}^{0} - \: 50° + 90° + 110° \:$

$\sf \: 360 {}^{0} - \sf \: 250 {}^{0}$

${ \red{ \sf \: \bold{110 {}^{0} }}}$

Hence, the Fourth Angle is 110°

Hence vertified.

Answer 2

Given

Angles of quadrilateral are 50° , 110° , 90° and x°

What To Find

Measure of angle x

Concept

When the sides of a quadrilaterals are extended and the exterior angles are produced. The sum of four exterior angle is always 360 degrees.

Solution

According to the Concept

50° + 110° + 90° + x = 360°

$\large\bf{\purple{ \leadsto}} \rm \: 50 \degree \: + \: 110 \degree \: + \: 90 \degree \: + \: x \degree \: = \: 360 \degree$

$\large\bf{\purple{ \leadsto}} \rm \: 250 \degree \: + \: x \: = \: 360 \degree \:$

$\large\bf{\purple{ \leadsto}} \rm \: x \: = \: 360 \degree \: - \: 250 \degree$

$\large\bf{\purple{ \leadsto}} \rm \: x \: = \: 110 \degree$

Hence , the measure of x is 110°