Exam 10: Probability and Counting Techniques

$\text { Classify the angle as acute, right, obtuse, or straight. }$

$\text { Find the measure of } \angle 1 \text { through } \angle 7 \text { if } \mathrm { m } \angle 8 = 55 ^ { \circ } \text {. }$

Which of the following is not a way to name the angle shown? A) $\angle P Q R$ B) $\angle R Q P$ C) $\angle 4$ D) $\angle P$

Find the measure of the supplement of $109 ^ { \circ }$ . A) $251 ^ { \circ }$ B) $71 ^ { \circ }$ C) $199 ^ { \circ }$ D) $19 ^ { \circ }$

$\text { Identify the quadrilateral. }$

In triangle $A B C$ , angle $C$ is a right angle. Find the measure of side $a$ if the measure of angle $B$ is $82 ^ { \circ }$ and side $c = 50$ in.

Find the measure of angle $C$ . A) $30 ^ { \circ }$ В) $35 ^ { \circ }$ C) $40 ^ { \circ }$ D) $25 ^ { \circ }$

Find the volume of the rectangular solid. A) $396 \mathrm { ft } ^ { 3 }$ B) $112 \mathrm { ft } ^ { 3 }$ C) $792 \mathrm { ft } ^ { 3 }$ D) $518 \mathrm { ft } ^ { 3 }$

In triangle $A B C$ , angle $C$ is a right angle. Find the measure of side $a$ if the measure of angle $A$ is $3 ^ { \circ }$ and side $b = 70 \mathrm { ft }$ .

An airplane flying at an altitude of 7200 feet sights the angle of depression to a control tower to be $18 ^ { \circ }$ . Find the horizontal distance the plane is from the control tower. (Disregard the height of the tower and round your answer to the nearest foot.) A) $\approx 23,301 \mathrm { ft }$ B) $\approx 7,570 \mathrm { ft }$ C) $\approx 2,339 \mathrm { ft }$ D) $\approx 22,159 \mathrm { ft }$

In elliptic geometry, how many lines can be drawn parallel to a given line through a point not on the given line?

$\text { Identify angles } 6 \text { and } 7 \text { as alternate interior, alternate exterior, corresponding, or vertical. }$

Find the surface area and volume. Use $3.14$ for $\pi$ .