Question

what is the missing angle in the triangle?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the missing angle be \(x\). We know one angle is 20°. Assume the other two - angle information is not given.

$$x + 20^{\circ}+y + z=180^{\circ}$$

If we assume the triangle is a non - degenerate triangle and we are only given one angle, and we assume the other two angles are non - zero. In the simplest case, if we consider a triangle with one known angle of 20° and assume the other two angles are equal (isosceles triangle case for simplicity, though not necessary), let the other two equal angles be \(a\) each. Then \(20^{\circ}+2a = 180^{\circ}\).

Step2: Solve for the missing angle

First, subtract 20° from both sides of the equation \(20^{\circ}+2a = 180^{\circ}\).

$$2a=180^{\circ}- 20^{\circ}=160^{\circ}$$

Then divide both sides by 2.

$$a = 80^{\circ}$$

If we consider the general case where we have one angle of 20° and no other information about the other two angles, and we want to find the third angle when the other two angles are combined, the third angle \(x\) satisfies \(x=180^{\circ}-20^{\circ}=160^{\circ}\) (assuming the other two angles together form a single non - split entity for the purpose of finding the remaining part of the 180° sum).

Answer:

160°