Question

question #4
what is the value of a?

Explanation:

Step1: Find the non - marked angle in the right - triangle

In a right - triangle, the sum of angles is \(180^{\circ}\). One angle is \(90^{\circ}\) and another is \(37^{\circ}\). So the non - marked angle is \(180-(90 + 37)=53^{\circ}\).

Step2: Use the linear - pair relationship

The angle \((2a - 7)\) and the \(53^{\circ}\) angle form a linear pair. So \(2a-7+53 = 180\).
Simplify the equation: \(2a+46 = 180\).
Subtract \(46\) from both sides: \(2a=180 - 46\), \(2a = 134\).
Divide both sides by \(2\): \(a=\frac{134}{2}\).

Answer:

\(a = 67\)