Question

find the measure of ∠2.
m∠2 =
(type a whole number.)

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Consider the triangle with angles 37°, 116°, and the third - angle (let's call it \(x\)). So, \(x = 180-(37 + 116)=180 - 153=27^{\circ}\).

Step2: Find the adjacent angle to 48°

The angle adjacent to 48° in the same triangle as the 116° and 37° angles is \(180 - 48=132^{\circ}\).

Step3: Consider the large triangle containing ∠2

In the large triangle containing ∠2, we know one angle is 74° and another angle is the one we found in Step1 which is 27°.
Using the angle - sum property of a triangle again, for the triangle with ∠2, we have \(m\angle2=180-(74 + 27)\).

Step4: Calculate the measure of ∠2

\(m\angle2=180-(74 + 27)=180 - 101 = 79^{\circ}\)

Answer:

79