Question

what is the measure of angle b? round to the tenth.*

Explanation:

Step1: Find angle \(a\)

Since \(a\) and \(116^{\circ}\) are supplementary angles (they form a linear - pair), \(a = 180^{\circ}-116^{\circ}=64^{\circ}\)

Step2: Use the triangle - like figure (the sum of angles in a quadrilateral - like figure with one right - angle (\(90^{\circ}\)) and three other angles: \(82^{\circ}\), \(a\), \(b\))

The sum of angles around the non - parallel lines (using the property of the sum of angles in a polygon - like structure formed by the transversals and the parallel - like lines in the figure). The sum of the angles in the four - angled figure (with one \(90^{\circ}\) angle) is \(360^{\circ}\). So, \(82^{\circ}+90^{\circ}+a + b=360^{\circ}\)
Substitute \(a = 64^{\circ}\) into the equation: \(82^{\circ}+90^{\circ}+64^{\circ}+b=360^{\circ}\)
First, calculate \(82 + 90+64=236\). Then the equation becomes \(236^{\circ}+b=360^{\circ}\)
Solve for \(b\): \(b=360^{\circ}-236^{\circ}=124^{\circ}\)

Answer:

\(124.0^{\circ}\)