a side of the triangle below has been extended to form an exterior angle of 125°. find the value of x.
a side of the triangle below has been extended to form an exterior angle of 125°. find the value of x.
Answer
Explanation:
Step1: Use 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. In this right - angled triangle, the exterior angle (125^{\circ}) is equal to the sum of the right angle ((90^{\circ})) and the angle (x). So, we can write the equation (x + 90^{\circ}=125^{\circ}).
Step2: Solve for (x)
Subtract (90^{\circ}) from both sides of the equation (x + 90^{\circ}=125^{\circ}). [ \begin{align*} x&=125^{\circ}- 90^{\circ}\ x&=35^{\circ} \end{align*} ]
Answer:
(x = 35)