Question

if three of the interior angles of a convex quadrilateral measure 93°, 140°, and 79°, find the measure of the fourth interior angle. degrees question 8 1 pts calculate the measure of each exterior angle of a regular 30 - gon. degrees

Explanation:

Step1: Find the sum of interior angles of a quadrilateral

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

Step2: Calculate the fourth interior angle

Let the fourth interior angle be \(x\). Then \(x=360-(93 + 140+79)\)
\(x = 360 - 312\)
\(x = 48^{\circ}\)

Step3: Recall the formula for the measure of an exterior angle of a regular polygon

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular \(n -\)gon, the measure of each exterior angle \(E=\frac{360^{\circ}}{n}\)

Step4: Calculate the measure of each exterior angle of a regular 30 - gon

Here \(n = 30\), so \(E=\frac{360}{30}=12^{\circ}\)

Answer:

48
12