Question

Use the triangle shown.

The diagram is a triangle. The Base of the triangle is largest side of the triangle. The opposite angle of largest side is denoted by 3. The right side angle is denoted by 2. The base side is extended to the left with arrow at the left end. The obtuse angle created by that extended line is denoted by 1.

If m∠1 = 98° and m∠2 = 19°, what is m∠3?

m∠3 =
°

Answer 1

To find the measure of angle \( m∠3 \), we can use the property that the sum of the angles in a triangle is \( 180^\circ \).

We are given:
- \( m∠2 = 19^\circ \)
- \( m∠1 = 98^\circ \) (angle outside the triangle that is formed by extending the base)

Since angles \( m∠1 \) and \( m∠2 \) are not part of the triangle, we must also note that \( m∠1 \) and \( m∠3 \) are related due to their corresponding positions.

The external angle \( m∠1 \) can be expressed in terms of the angles of the triangle:
\[
m∠1 = m∠2 + m∠3
\]
Substituting the known values:
\[
98^\circ = 19^\circ + m∠3
\]
Now, we can solve for \( m∠3 \):
\[
m∠3 = 98^\circ - 19^\circ
\]
\[
m∠3 = 79^\circ
\]

Thus, the measure of angle \( m∠3 \) is:
\[
\boxed{79^\circ}
\]