Question

example 1 check your turn!
use the triangle angle sum theorem
ex find the measure of each numbered angle.
find m
74 + 43 = 117
180 - 117 = 63°
m∠1 = 63° m∠2 = 63° m∠3 = 38°
(image: two triangles with angles 43°, 74° in one and 79° in the other, and angles 1, 2, 3. question: \what do you notice about the two angles across from each other?\)

Explanation:

Step1: Find \( m\angle1 \)

The sum of angles in a triangle is \( 180^\circ \). For the triangle with angles \( 43^\circ \), \( 74^\circ \), and \( \angle1 \), we use the formula:
\( m\angle1 + 43^\circ + 74^\circ = 180^\circ \)
Simplify: \( m\angle1 = 180^\circ - 43^\circ - 74^\circ = 63^\circ \).

Step2: Find \( m\angle2 \)

\( \angle1 \) and \( \angle2 \) are vertical angles, so they are equal. Thus, \( m\angle2 = m\angle1 = 63^\circ \).

Step3: Find \( m\angle3 \)

For the triangle with angles \( 79^\circ \), \( \angle2 \) (which is \( 63^\circ \)), and \( \angle3 \), use the triangle angle sum:
\( m\angle3 + 79^\circ + 63^\circ = 180^\circ \)
Simplify: \( m\angle3 = 180^\circ - 79^\circ - 63^\circ = 38^\circ \).

Answer:

\( m\angle1 = \boldsymbol{63^\circ} \), \( m\angle2 = \boldsymbol{63^\circ} \), \( m\angle3 = \boldsymbol{38^\circ} \)