Question

the figures below are congruent. find \z\.
question 3
answer:

Explanation:

Step1: Use the angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^{\circ}\).

Step2: Set up the equation

Let the angles of the first quadrilateral be \(a = 115^{\circ}\), \(b=45^{\circ}\), \(c = 20^{\circ}\), and the fourth angle (which is equal to \(z\) since the figures are congruent) be \(d\). Then \(a + b + c + d=360^{\circ}\). Substituting the values: \(115^{\circ}+45^{\circ}+20^{\circ}+z = 360^{\circ}\).

Step3: Solve for \(z\)

First, add the known angles: \(115 + 45+20=180\). So the equation becomes \(180^{\circ}+z = 360^{\circ}\). Then \(z=360^{\circ}-180^{\circ}\).

Answer:

\(180^{\circ}\)