Question

if three of the interior angles of a convex quadrilateral measure 99°, 122°, and 77°, find the measure of the fourth interior angle. degrees question 26 1 pts calculate the measure of each exterior angle of a regular pentagon. degrees

Explanation:

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

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

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

We know that \(99^{\circ}+122^{\circ}+77^{\circ}+x = 360^{\circ}\).

Step3: Simplify the left - hand side

\(99 + 122+77+x=(99 + 122)+77+x=221+77+x = 298+x\).

Step4: Solve for \(x\)

Since \(298+x = 360\), then \(x=360 - 298=62^{\circ}\).

Step5: Recall the formula for the measure of each exterior angle of a regular polygon

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular pentagon (\(n = 5\)), the measure of each exterior angle \(y=\frac{360^{\circ}}{n}\).

Step6: Calculate the measure of each exterior angle of a regular pentagon

Substitute \(n = 5\) into the formula, \(y=\frac{360^{\circ}}{5}=72^{\circ}\).

Answer:

62
72