Question

topic 7: triangles and an

1. find the measure of each numbered angle.
2. find t

(figure with a right triangle and another triangle, angles labeled 1, 2, 3, 43°, 28°, right angle; handwritten notes: 180°, ∠1=43+90=133→180-133=47, 43+28=71, 180-71=109; m∠1 = 47, m∠2 = 43°, m∠3 = 109
(another table with m(ab), m(cd), types, partially visible)
© gina wilson (all things alge

Explanation:

Step1: Find \( m\angle1 \)

The left triangle is a right triangle (one angle is \( 90^\circ \)). The angle adjacent to \( \angle1 \) and \( 43^\circ \) should sum to \( 90^\circ \) (since it's a right triangle). Wait, actually, in the right triangle, the angles are \( 90^\circ \), \( 43^\circ \), and \( \angle1 \)? Wait, no, looking at the diagram, the left triangle has a right angle, \( 43^\circ \), and \( \angle1 \). Wait, the sum of angles in a triangle is \( 180^\circ \). So for the right triangle: \( 90^\circ + 43^\circ + \angle1 = 180^\circ \)? Wait, no, maybe the angle \( \angle1 \) is complementary to \( 43^\circ \) because of the right angle. Wait, the right angle is \( 90^\circ \), so \( \angle1 + 43^\circ = 90^\circ \)? Wait, no, let's re-examine. The diagram shows a right angle (square corner), \( 43^\circ \), and \( \angle1 \) in the left triangle? Wait, maybe the left triangle has angles \( 90^\circ \), \( 43^\circ \), and \( \angle1 \), so \( \angle1 = 180^\circ - 90^\circ - 43^\circ = 47^\circ \). So \( m\angle1 = 47^\circ \).

Step2: Find \( m\angle2 \)

Wait, maybe \( \angle2 \) is equal to \( 43^\circ \)? Wait, no, looking at the diagram, the angle with \( 43^\circ \) and \( \angle2 \) – maybe \( \angle2 \) is equal to \( 43^\circ \)? Wait, no, maybe the right triangle has \( 90^\circ \), \( \angle1 \), and \( 43^\circ \), so \( \angle1 = 47^\circ \), and then \( \angle2 \) – wait, maybe the angle adjacent to \( \angle1 \) and \( \angle3 \) is a straight line (180°). Wait, no, let's check the other triangle. The right triangle (the one with \( 28^\circ \)): sum of angles is \( 180^\circ \). So \( \angle3 + 28^\circ + \) the other angle. Wait, the other angle in that triangle: since the left triangle has a right angle, the angle at the bottom left (the common vertex) – maybe \( \angle2 \) is equal to \( 43^\circ \)? Wait, the original work has \( m\angle2 = 43^\circ \), maybe because it's a vertical angle or alternate interior? Wait, maybe \( \angle2 = 43^\circ \) as per the diagram's markings.

Step3: Find \( m\angle3 \)

In the triangle with \( 28^\circ \) and \( \angle2 = 43^\circ \), the sum of angles is \( 180^\circ \). So \( \angle3 + 28^\circ + 43^\circ = 180^\circ \). So \( \angle3 = 180^\circ - 28^\circ - 43^\circ = 109^\circ \). Wait, but \( 28 + 43 = 71 \), \( 180 - 71 = 109 \), so \( m\angle3 = 109^\circ \). Wait, but the original work has \( 43 + 90 = 133 \), \( 180 - 133 = 47 \) for \( \angle1 \), which matches our first step. Then \( \angle2 = 43^\circ \), and \( \angle3 = 180 - 28 - 43 = 109^\circ \).

Answer:

\( m\angle1 = \boldsymbol{47^\circ} \), \( m\angle2 = \boldsymbol{43^\circ} \), \( m\angle3 = \boldsymbol{109^\circ} \)