Question

find each lettered angle measure. (round to the first decimal place if needed)
what is the measure of angle a? *
1 point
your answer

Explanation:

Step1: Use the polygon exterior angle sum theorem

The sum of exterior angles of any polygon is \(360^{\circ}\).
Let the measure of angle \(a\) be \(x\). Then we have the equation \(x + 68^{\circ}+84^{\circ}+60^{\circ}+(180 - 140)^{\circ}=360^{\circ}\).
First, simplify \((180 - 140)^{\circ}=40^{\circ}\).
The equation becomes \(x+68 + 84+60 + 40=360\).

Step2: Solve for \(x\)

Combine the known angles: \(68+84 + 60+40=(68 + 84)+(60 + 40)=152+100 = 252\).
Then \(x=360 - 252\).
\(x = 108^{\circ}\).

Answer:

\(108^{\circ}\)