Question

if three of the interior angles of a convex quadrilateral measure 100°, 132°, and 70°, find the measure of the fourth interior angle.
____ degrees

Explanation:

Step1: Recall the sum of interior angles formula

The sum of interior angles of a convex quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Set up an equation

Let the fourth - angle measure be \(x\). Then \(100^{\circ}+132^{\circ}+70^{\circ}+x = 360^{\circ}\).

Step3: Solve for \(x\)

First, add the known angles: \(100 + 132+70=302\). Then \(x=360 - 302\).

Answer:

\(58\)