Question

solve for the missing angle.

Explanation:

Step1: Find the adjacent angle of \(110^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the adjacent angle of \(110^{\circ}\) is \(180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Use the triangle - angle sum property

In \(\triangle TSU\), the sum of interior angles of a triangle is \(180^{\circ}\). Let the missing angle be \(x\). We know one angle is \(80^{\circ}\) and another is \(70^{\circ}\). Then \(x + 80^{\circ}+70^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(80^{\circ} + 70^{\circ})$$

$$x = 180^{\circ}-150^{\circ}$$

Answer:

\(30^{\circ}\)