Question

Find the measure of x in the following figure:​

Answer 1

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Answer 2

Given:

• First angle = 140°

• Second angle = x

• Third angle = ?

• Fourth angle = 60°

To calculate:

• Value of x.

Clarification:

Here, we are provided a diagram of a quadrilateral. In which, the value of 2 angles are given and value of 2 angles aren't given. Measure of 1st angle is 140°, measure of fourth angle is 60°. We haven't the value of second angle and third angle. According to the question, we have to find the value of second angle (x). So,

• At first we'll find the measure of third angle by linear pair property.

• Then, we'll find the measure of x by the using the angle sum property of a quadrilateral and by forming an algebraic equation.

• By solving that equation we'll find the measure of second angle.

Calculation:

Let,

• 140° → First angle
• x → Second angle
• y → Third angle
• 60° → Fourth angle

By linear pair,

$\longrightarrow \sf {3rd \:angle + {130}^{\circ} = {180}^{\circ} }$

$\longrightarrow \sf {3rd \:angle = {180}^{\circ} -{130}^{\circ} }$

$\longrightarrow \sf {3rd \:angle = {180}^{\circ} -{130}^{\circ} }$

$\longrightarrow \sf {3rd \:angle ={50}^{\circ} }$

Now, we have :

• First angle = 140°

• Second angle = x

• Third angle = 50°

• Fourth angle = 60°

As we know that,

» Sum of the angles of a quadrilateral = 360°

$\longrightarrow \sf {1st \: angle + 2nd \: angle + 3rd \: angle + 4th \: angle = {360}^{\circ} }$

$\longrightarrow \sf { {140}^{\circ} + {x}^{\circ} + {50}^{\circ} + {60}^{\circ} = {360}^{\circ} }$

$\longrightarrow \sf { {250}^{\circ} + {x}^{\circ} = {360}^{\circ} }$

$\longrightarrow \sf { {x}^{\circ} = {360}^{\circ}- {250}^{\circ} }$

$\longrightarrow \boxed{\sf \red{ {x}^{\circ} = {110}^{\circ}} }$

Henceforth, value of x is 110°.

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