Question

ghij ~ uvwx. what is m∠w?
(there are two quadrilaterals: ghij with angles at g: 135°, at i: 95°; uvwx with angle at v: 43°, at x: 87°. we need to find m∠w.)
m∠w = \boxed{\space}°

Explanation:

Step1: Recall the property of similar polygons

Similar polygons have corresponding angles equal. The sum of interior angles of a quadrilateral is \(360^{\circ}\).

Step2: Set up the angle - sum equation

For quadrilateral \(GHIJ\) and \(UVWX\), since \(GHIJ\sim UVWX\), let \(m\angle W = x\).
We know that \(135^{\circ}+95^{\circ}+43^{\circ}+x = 360^{\circ}\) (sum of interior angles of a quadrilateral).

Step3: Solve the equation for \(x\)

First, add the known angles: \(135 + 95+43=273\).
Then, \(x=360 - 273\).

Answer:

\(87\)