Question

a side of the triangle below has been extended to form an exterior angle of 70°. find the value of x.
answer
x =

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
Let the exterior angle be \(E = 70^{\circ}\), one non - adjacent interior angle be \(A=46^{\circ}\), and the other non - adjacent interior angle be \(x\).
According to the exterior - angle property \(E=x + 46^{\circ}\).

Step2: Solve for \(x\)

Rearrange the equation \(70^{\circ}=x + 46^{\circ}\) to find \(x\).
Subtract \(46^{\circ}\) from both sides of the equation: \(x=70^{\circ}-46^{\circ}\).

$$x = 24^{\circ}$$

Answer:

\(24\)