Question

what is the measure of \\( \angle b \\)?
\\( 98 ^ { \circ } \\)
\\( 108 ^ { \circ } \\)
\\( 118 ^ { \circ } \\)
\\( 128 ^ { \circ } \\)

Explanation:

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

The sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a hexagon (\(n=6\)), the sum \(S=(6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Calculate the measure of \(\angle B\)

Let \(\angle B=x\). We know \(\angle A = 170^{\circ}\), \(\angle C=133^{\circ}\), \(\angle D = 102^{\circ}\), \(\angle E=117^{\circ}\), \(\angle F = 90^{\circ}\).
Using the sum of interior angles formula: \(x+170^{\circ}+133^{\circ}+102^{\circ}+117^{\circ}+90^{\circ}=720^{\circ}\).
Simplify the left - hand side: \(x+(170 + 133+102+117+90)=x + 612^{\circ}\).
Then \(x=720^{\circ}-612^{\circ}\).

Answer:

\(108^{\circ}\)