Question

for the figure shown, find m∠1 and m∠2. (the figure is not drawn to scale.) m∠1 = □°

Explanation:

Step1: Use exterior - angle property for ∠1

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the larger triangle, the exterior angle is 130°. So, \(m\angle1+18^{\circ}=130^{\circ}\).
\[m\angle1 = 130^{\circ}-18^{\circ}\]

Step2: Calculate the value of ∠1

\[m\angle1=112^{\circ}\]

Step3: Use angle - sum property for the smaller triangle to find ∠2

In the smaller triangle, we know one angle is \(27^{\circ}\) and another is \(m\angle1 = 112^{\circ}\). The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle2=x\), then \(27^{\circ}+x + 112^{\circ}=180^{\circ}\).
\[x=180^{\circ}-(27^{\circ}+112^{\circ})\]
\[x = 180^{\circ}-139^{\circ}\]
\[m\angle2 = 41^{\circ}\]

Answer:

\(m\angle1 = 112^{\circ}\), \(m\angle2 = 41^{\circ}\)