Question

what is the value of a?
2a + 25°
5a
35°
a =
submit

Explanation:

Step1: Apply the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(5a=(2a + 25^{\circ})+35^{\circ}\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation: \((2a + 25^{\circ})+35^{\circ}=2a+(25^{\circ}+35^{\circ})=2a + 60^{\circ}\). So the equation becomes \(5a=2a + 60^{\circ}\).

Step3: Solve for \(a\)

Subtract \(2a\) from both sides of the equation: \(5a-2a=2a + 60^{\circ}-2a\). This gives \(3a=60^{\circ}\). Then divide both sides by 3: \(a=\frac{60^{\circ}}{3}\).

Answer:

\(20\)