Question

the diagram shows a triangle.
what is the value of a?
a = \boxed{\space}^\circ

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(53^\circ + 61^\circ + 3a = 180^\circ\).

Step2: Calculate sum of known angles

Add \(53^\circ\) and \(61^\circ\): \(53 + 61 = 114\). So, \(114^\circ + 3a = 180^\circ\).

Step3: Solve for \(3a\)

Subtract \(114^\circ\) from both sides: \(3a = 180 - 114 = 66\).

Step4: Solve for \(a\)

Divide both sides by 3: \(a = \frac{66}{3} = 22\).

Answer:

\(22\)