Question

1. two angles of a quadrilateral measure 132°. if the measure of a third angle is 75°, what is the measure of the remaining angle?

Explanation:

Step1: Recall quadrilateral angle sum

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

Step2: Calculate sum of known angles

Two angles are \(132^\circ\) each, and one is \(75^\circ\). So sum of known angles: \(132^\circ\times2 + 75^\circ = 264^\circ + 75^\circ = 339^\circ\).

Step3: Find the remaining angle

Subtract sum of known angles from \(360^\circ\): \(360^\circ - 339^\circ = 21^\circ\).

Answer:

The measure of the remaining angle is \(21^\circ\).