Question

challenge given that ( mangle a=(18x)^{circ}), ( mangle c=(8x + 28)^{circ}), and ( mangle d = 118^{circ}), what is ( mangle b)?
( mangle b=square^{circ})
(the figure is not drawn to

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So, \(m\angle D=m\angle A + m\angle C\).
Substitute \(m\angle A=(18x)^{\circ}\), \(m\angle C=(8x + 28)^{\circ}\), and \(m\angle D = 118^{\circ}\) into the equation:
\(118=18x+(8x + 28)\)

Step2: Simplify the equation

Combine like terms:
\(118=18x+8x + 28\)
\(118=26x+28\)
Subtract 28 from both sides:
\(118 - 28=26x+28 - 28\)
\(90=26x\)
Solve for \(x\):
\(x=\frac{90}{26}=\frac{45}{13}\)

Step3: Find \(m\angle B\)

Since \(m\angle B\) and \(m\angle D\) are supplementary (they form a linear pair), \(m\angle B=180 - m\angle D\)
\(m\angle B = 180-118\)
\(m\angle B = 62^{\circ}\)

Answer:

\(62\)