Question

find the measures of angles 1, 2, and 3. (the figure is not to scale.) then find m∠1 then m∠2 and then m∠3. the measure of angle 1 is (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Find \(m\angle1\)

Let's assume the three angles of the triangle are \(m\angle1\), \(m\angle2\), and \(m\angle3\). We know two of the angles are 81° and 40°. So, \(m\angle1=180-(81 + 40)\).
\[m\angle1=180 - 121=59^{\circ}\]

Step3: Find \(m\angle2\)

From the figure, we can see that \(m\angle2\) and the 81° angle are vertical - angles. Vertical angles are equal. So, \(m\angle2 = 81^{\circ}\).

Step4: Find \(m\angle3\)

We already found \(m\angle1 = 59^{\circ}\) and \(m\angle2=81^{\circ}\). Using the angle - sum property of a triangle (\(m\angle1 + m\angle2+m\angle3=180^{\circ}\)), we can also find \(m\angle3\) as \(m\angle3 = 40^{\circ}\) (since we used the fact that the sum of the given non - \(\angle3\) angles in the triangle is 121° to find \(\angle1\) and the other non - \(\angle1\) and non - \(\angle2\) angle is 40°).

Answer:

\(m\angle1 = 59^{\circ}\), \(m\angle2 = 81^{\circ}\), \(m\angle3 = 40^{\circ}\)