Question

Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of each of the equal angles.

Answer 1

Answer:

Given :

Three angles of a quadrilateral are equal.

Third angle =120°

To find :

Measure of each of the equal angle =?

Solution :

Let the three equal angles be a, b, c.

a=b=c=x°

Sum of all the angles of a quadrilateral =360°

According to the question,

a+b+c+d+120=360

3x+120=360

3x=360-120

3x=240

x = 240/3 = 80°

$Hence \: x (measure of each angle)\\ \: is \: equal \: to \: 80°$

Answer 2

$\large \bigstar\boxed{\bf \red{ GIVEN}} \bigstar \\ \\ \Longrightarrow \bf\angle1 = x \\\Longrightarrow \bf\angle2= x \\\Longrightarrow \bf\angle3 = x \\\Longrightarrow \bf\angle4 = 120$

$\large \bigstar\boxed{\bf \red{ TO \: FIND}} \bigstar \\ \\ \bf\Longrightarrow Value \: of \: all \: angles$

$\large \bigstar\boxed{\bf \red{ SOLUTION}} \bigstar \\ \\\Longrightarrow \bf\angle1 + \angle2 + \angle3 + \angle4 = 360 \\ \\\Longrightarrow \bf x + x + x + 120 = 360 \\ \\\Longrightarrow \bf 3x = 360 - 120 \\ \\ \bf\Longrightarrow x = \frac{240}{3} \\ \\ \huge \boxed{ \bf \orange {x = 80°}}$