Solve for X: Finding Angles in an Isosceles Trapezoid with 120° Given

Question

Given: $∢C=2x$

$∢A=120°$

isosceles trapezoid.

Find x.

00:00 Find X

00:03 An isosceles trapezoid according to the given data

00:09 In a trapezoid, angles on the same leg sum to 180

00:20 Substitute the value of A to find X

00:31 Isolate angle X

00:46 And this is the solution to the question

Given that the trapezoid is isosceles and the angles on both sides are equal, it can be argued that:

$∢C=∢D$

$∢A=∢B$

We know that the sum of the angles of a quadrilateral is 360 degrees.

Therefore we can create the formula:

$∢A+∢B+∢C+∢D=360$

We replace according to the existing data:

$120+120+2x+2x=360$

$240+4x=360$

$4x=360-240$

$4x=120$

We divide the two sections by 4:

$\frac{4x}{4}=\frac{120}{4}$

$x=30$

30°