a side of the triangle below has been extended to form an exterior angle of 145°. find the value of x.
a side of the triangle below has been extended to form an exterior angle of 145°. find the value of x.
Answer
Explanation:
Step1: Use the property of supplementary angles
The exterior angle of (145^{\circ}) and the adjacent interior angle form a linear - pair (supplementary angles). Let the adjacent interior angle be (y). Then (x + y=180^{\circ}), so (y = 180 - 145).
Step2: Use the angle - sum property of a triangle
The sum of angles in a triangle is (180^{\circ}). The triangle has angles (x), (y), and (90^{\circ}). So (x+y + 90=180). Since (y=180 - 145 = 35), substituting (y) into (x+y + 90=180) gives (x+35 + 90=180). Then (x=180-(35 + 90)). Another way: Using the exterior - angle property (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles). The exterior angle of (145^{\circ}) is equal to the sum of the right angle ((90^{\circ})) and (x). So (x+90 = 145).
Answer:
(x = 55)