Question

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

Explanation:

Step1: Use the angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Consider the large triangle. First, find the third - angle of the large triangle with angles 37° and 116°. Let this angle be \(x\). Then \(x=180-(37 + 116)=180 - 153 = 27^{\circ}\).

Step2: Consider the small triangle containing \(\angle2\)

In the small triangle containing \(\angle2\), we know one angle is 78° and the other angle is \(27^{\circ}\) (from Step 1). Let \(\angle2 = y\). Using the angle - sum property of a triangle (\(y+78 + 27=180\)).

Step3: Solve for \(\angle2\)

\[y=180-(78 + 27)=180 - 105=75^{\circ}\]

Answer:

75