10.2.0: Exercises

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Classify the angles in the following exercises as acute, obtuse, right, or straight.

Exercise $\PageIndex{1}$

$m\measuredangle = {32^ \circ }$

Exercise $\PageIndex{2}$

$m\measuredangle = {120^ \circ }$

Exercise $\PageIndex{3}$

$m\measuredangle = {180^ \circ }$

Exercise $\PageIndex{4}$

$m\measuredangle = {90^ \circ }$

Exercise $\PageIndex{5}$

$m\measuredangle = {110^ \circ }$

Exercise $\PageIndex{6}$

$m\measuredangle = {45^ \circ }$

Exercise $\PageIndex{7}$

Use the given figure to solve for the angle measurements.

$Two lines intersect each other forming a right angle. A ray originates from the intersection point of the lines. The ray makes an acute angle, 5 x plus 4 with the horizontal line. The ray makes an acute angle, 39 x minus 2 with the vertical line.$

Exercise $\PageIndex{8}$

Use the given figure to solve for the angle measurements.

$A horizontal line with two rays originating from its center. The first ray makes an angle, 3 x plus 2 with the horizontal axis. The angle formed between the two rays is labeled 3 x plus 7. The second ray makes an angle, 2 x plus 3 with the horizontal axis.$

Exercise $\PageIndex{9}$

Give the measure of the supplement to ${89^ \circ }.$

Use the given figure for the following exercises. Let angle 2 measure ${35^ \circ }$.

$Two parallel lines, l subscript 1 and l subscript 2 are intersected by a transversal. The transversal makes four angles numbered 1, 2, 3, and 4 with the line, l subscript 1. The transversal makes four angles numbered 5, 6, 7, and 8 with the line, l subscript 2. 1, 2, 7, and 8 are exterior angles. 3, 4, 5, and 6 are interior angles.$

Exercise $\PageIndex{10}$

Find the measure of angle 1 and state the reason for your solution.

Exercise $\PageIndex{11}$

Find the measure of angle 3 and state the reason for your solution.

Exercise $\PageIndex{12}$

Find the measure of angle 4 and state the reason for your solution.

Exercise $\PageIndex{13}$

Find the measure of angle 5 and state the reason for your solution.

Exercise $\PageIndex{14}$

Find the measure of angle 6 and state the reason and state the reason for your solution.

Exercise $\PageIndex{15}$

Find the measure of angle 7 and state the reason for your solution.

Exercise $\PageIndex{16}$

Find the measure of angle 8 and state the reason for your solution.

Exercise $\PageIndex{17}$

Use the given figure to solve for the angle measurements.

$Two lines intersect each other. One set of opposite angles is labeled 5 x minus 129 and 2 x minus 21.$

Use the given figure for the following exercises.

$Two parallel lines are intersected by a transversal. The transversal makes four angles with the line, l subscript 1. Two angles are unknown. Two opposite angles are marked 3 and 50 degrees. The transversal makes four angles with the line, l subscript 2. 8 and 50 degrees are exterior angles. 3 is the interior angle.$

Exercise $\PageIndex{18}$

Find the measure of angle 3 and explain the reason for your solution.

Exercise $\PageIndex{19}$

Find the measure of angle 8 and explain the reason for your solution.

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