Questions: Determine the measures of the angles using the diagram below. 1: 2: 3: 4:

Transcript text: Determine the measures of the angles using the diagram below. $1:$ $\square$ $2:$ $\square$ 3: $\square$ 4: $\square$

Solution

Solution Steps

Step 1: Find the measure of angle 2.

Angles 2, 30°, and 76° form a straight line, therefore they add up to 180°. Angle 2 = 180° - 30° - 76° = 74°

Step 2: Find the measure of angle 1.

Since _l_ and _m_ are parallel, angle 1 and the combined angle of 30° and 76° are congruent corresponding angles. Angle 1 = 30° + 76° = 106°

Step 3: Find the measure of angle 3.

Since line _n_ is a straight line, angles 2 and 3 are supplementary and add up to 180°. Angle 3 = 180° - 74° = 106°

Step 4: Find the measure of angle 4.

Since _l_ and _m_ are parallel, and _n_ is a transversal, angle 4 and the combined angle of 30° and 76° are congruent corresponding angles. Angle 4 = 30° + 76° = 106°

Final Answer:

1: 106° 2: 74° 3: 106° 4: 106°

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