Question

The four angles of a quadrilateral are (xº + 50°), (3x°-30°),(x°÷2+70°) and (2x°+10°). find each angle ​

Answer 1

Given :-

First angle of the quadrilateral = (xº + 50°)

Second angle of the quadrilateral = (3x°-30°)

Third angle of the quadrilateral = (x°/2+70°)

Fourth angle of the quadrilateral = (2x°+10°)

To Find :-

The first angle.

The second angle.

The third angle.

The fourth angle.

Analysis :-

We know that the total degree of a quadrilateral is 360°.

Make an equation and get the value of the variable in the question.

Substitute the value of the variable in each of the angle.

Solution :-

We know that,

Sum of the angles of quadrilateral = 360°

Making an equation,

$\sf (x+50)+(3x-30)+(\dfrac{x}{2} +70)+(2x+10)=360$

$\sf 13x+200=720$

By transposing 200,

$\sf 13x=720-200$

$\sf 13x=520$

Finding the value of x,

$\sf x=\dfrac{520}{13}$

$\sf x=40$

Finding the angles,

$\sf x+50=90^{o}$

$\sf 3x-30=90^{o}$

$\sf \dfrac{x}{2} +70=90^{o}$

$\sf 2x+10=90^{o}$

Therefore, each angles of the quadrilaterals measure 90°.