Question

In a quadrilateral sum of 3
angles are equal to twice the fourth angle. Find the fourth angle

Answer 1

Hi friend!

$<b><u><big><marquee direction="right"><big>Answer:</big></marquee></big></u></b>$

Let the four angles be $a, \: b, \: c \: and \: d.$

The sum of three angles
$a + b + c$

equals to (=) twice the fourth angle
$a + b + c = 2d$
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We know that sum of all angles = 360° (angle-sum of a quadrilateral)
$(a + b + c )+ d = 360° \\ \\ 2d + d = 360° \\ 3d = 360° \\ d = \frac{360°}{3} \\ d = 120°$

$The \: fourth \: angle = d = 120°$
$<hr size=5 color=blue> <p style="border:3px; border-style:solid; border-color:#00FF00; padding: 1em;"><big>Therefore, the fourth angle is <big><b>120°</b></big>.</big></p>$

Answer 2

Answer:

360 degree

Step-by-step explanation:

Let the angles be w,x,y,z

Sum of all angles = 360 degree

A.T.Q.

w + y + x + z =360 degree

3w = 360

w = 120 degree

4th angle