Question

the diagram shows a convex polygon. angles: 83°, 3a - 29°, 90°, 5a. what is the value of a? a = °

Explanation:

Step1: Recall the sum of exterior angles of a convex polygon.

The sum of the exterior angles of any convex polygon is \(360^\circ\). So we can set up the equation: \(83^\circ + (3a - 29)^\circ + 90^\circ + 5a^\circ = 360^\circ\).

Step2: Simplify the left - hand side of the equation.

First, combine like terms: \(83 - 29+90+(3a + 5a)=360\).
Calculate the constant terms: \(83-29 = 54\), then \(54 + 90=144\). And the variable terms: \(3a+5a = 8a\). So the equation becomes \(144 + 8a=360\).

Step3: Solve for \(a\).

Subtract 144 from both sides of the equation: \(8a=360 - 144\).
Calculate \(360-144 = 216\), so \(8a = 216\).
Then divide both sides by 8: \(a=\frac{216}{8}=27\).

Answer:

\(27\)