Question

the figure shown is a triangle with three unknown angles. to find out if the sum of the three interior angle measures of any triangle is 180°, show: m∠1 + m∠2 + m∠3 = 180° m∠1 = m∠4 m∠2 = m∠5 angles 3, 4, and 5 make a straight angle. rewrite the sum. m∠1 + m∠2 + m∠3 = m∠4 + m∠5 + m∠3 = ?

Explanation:

Step1: Recall straight angle measure

A straight angle measures \( 180^\circ \). Angles 3, 4, 5 form a straight angle, so \( m\angle3 + m\angle4 + m\angle5 = 180^\circ \).

Step2: Substitute equal angles

We know \( m\angle1 = m\angle4 \) and \( m\angle2 = m\angle5 \). Substitute \( m\angle4 \) with \( m\angle1 \) and \( m\angle5 \) with \( m\angle2 \) in \( m\angle3 + m\angle4 + m\angle5 \). So \( m\angle1 + m\angle2 + m\angle3 = m\angle4 + m\angle5 + m\angle3 = 180^\circ \).

Answer:

\( 180^\circ \)