Question

8.
triangle with angles 41° and 75°, and another right triangle with 54° angle. angles labeled 1, 2, 3. find m∠1, m∠2, m∠3

Explanation:

Step1: Find \( m\angle1 \)

The sum of the interior angles of a triangle is \( 180^\circ \). For the first triangle with angles \( 41^\circ \), \( 75^\circ \), and \( \angle1 \), we use the formula \( \text{Sum of angles} = 180^\circ \). So, \( m\angle1 = 180^\circ - 41^\circ - 75^\circ \).

$$ m\angle1 = 180 - 41 - 75 = 64^\circ $$

Step2: Find \( m\angle2 \)

Angles on a straight line sum to \( 180^\circ \), and there is a right angle (\( 90^\circ \)) and \( \angle1 = 64^\circ \). So, \( m\angle2 = 180^\circ - 90^\circ - 64^\circ \).

$$ m\angle2 = 180 - 90 - 64 = 26^\circ $$

Step3: Find \( m\angle3 \)

For the right - angled triangle with angles \( 54^\circ \), \( 90^\circ \), and \( \angle3 \), using the sum of interior angles of a triangle (\( 180^\circ \)), we have \( m\angle3 = 180^\circ - 90^\circ - 54^\circ \).

$$ m\angle3 = 180 - 90 - 54 = 36^\circ $$

Answer:

\( m\angle1 = 64^\circ \), \( m\angle2 = 26^\circ \), \( m\angle3 = 36^\circ \)