Question

what is the value of a? (diagram: triangle with angles ( a ), ( a - 50^circ ), and exterior angle ( a + 50^circ )) ( a = square^circ )

Explanation:

Step1: Identify the angle relationship

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the exterior angle is \(a + 50^{\circ}\), and the two non - adjacent interior angles are \(a\) and \(a-50^{\circ}\). So we can set up the equation:
\(a + 50^{\circ}=a+(a - 50^{\circ})\)

Step2: Simplify the equation

First, expand the right - hand side of the equation:
\(a + 50^{\circ}=a+a - 50^{\circ}\)
Then, subtract \(a\) from both sides of the equation:
\(a+50^{\circ}-a=a + a-50^{\circ}-a\)
We get \(50^{\circ}=a - 50^{\circ}\)

Step3: Solve for \(a\)

Add \(50^{\circ}\) to both sides of the equation \(50^{\circ}=a - 50^{\circ}\):
\(50^{\circ}+ 50^{\circ}=a-50^{\circ}+50^{\circ}\)
\(100^{\circ}=a\)

Answer:

\(100\)