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 question 12 1 pts calculate the measure of each interior angle of a regular decagon. degrees

Explanation:

Step1: Recall the formula for the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral \(S=(n - 2)\times180^{\circ}\), where \(n = 4\). So \(S=(4 - 2)\times180^{\circ}=360^{\circ}\)

Step2: Let the fourth - angle be \(x\)

We know that \(100^{\circ}+132^{\circ}+70^{\circ}+x = 360^{\circ}\)

Step3: Solve for \(x\)

First, calculate \(100 + 132+70=302\). Then \(x=360 - 302\)

Step1: Recall the formula for the sum of interior angles of a polygon

The sum of interior angles of a polygon \(S=(n - 2)\times180^{\circ}\), for a decagon \(n = 10\). So \(S=(10 - 2)\times180^{\circ}=1440^{\circ}\)

Step2: Calculate the measure of each interior angle of a regular decagon

Since a regular decagon has \(n = 10\) equal interior angles, each interior angle \(A=\frac{(n - 2)\times180^{\circ}}{n}\)
Substitute \(n = 10\) into the formula: \(A=\frac{(10 - 2)\times180^{\circ}}{10}\)

Step3: Simplify the expression

\((10 - 2)\times180^{\circ}=8\times180^{\circ}=1440^{\circ}\), then \(A = 144^{\circ}\)

Answer:

\(58\)

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