Launch Day Angle Checks

Use angle relationships to check model rocket equipment diagrams.

Read the Equipment Diagrams

All angle measures are in degrees. Use the stated relationships and labels, not measurements of the drawings. Write an equation on scratch paper for each blank.

A brace divides a right-angle corner of an equipment case.

Find x.

A support divides a straight angle on the launch-day diagram. Which equation finds x?

A. x = 117B. x + 117 = 180C. x + 117 = 90D. x − 117 = 180

Two straight lines cross on a tracking-screen diagram. A pair of vertical angles measures (6x + 8)° and 80°.

Find x.

Two adjacent viewing angles share a side and have no overlapping interiors. Their measures are 38° and 47°.

What is the measure of the combined angle? °

Two complementary angles on a bracket diagram measure (2x + 7)° and (x + 17)°. Which equation represents their relationship?

A. (2x + 7) − (x + 17) = 90B. (2x + 7) + (x + 17) = 180C. (2x + 7) + (x + 17) = 90D. 2x + 7 = x + 17

Solve the Angle Equations

Identify the angle relationship first. Be sure to report the requested value: x or an angle measure.

Two supplementary angles in a folding stand measure (4x + 12)° and (2x + 6)°.

What is the measure of the angle labeled (4x + 12)°? °

Two vertical angles formed by crossing alignment lines measure (5x − 9)° and (3x + 25)°. Which equation should be used to find x?

A. 5x − 9 = 3x + 25B. (5x − 9) + (3x + 25) = 180C. (5x − 9) + (3x + 25) = 90D. (5x − 9) − (3x + 25) = 180

Three adjacent angles fill a straight angle on a launch-pad plan. Their measures are 29°, x°, and (2x + 10)°. Their interiors do not overlap.

Find x.

A ray splits a 128° angle on a camera mount into two adjacent angles.

What is the measure of the angle labeled 2x°? °

10.

A straight cable guide is divided into two adjacent angles. One angle measures x° and the other measures 4x°. What is the smaller angle's measure?

A. 36°B. 45°C. 144°D. 18°

Check Launch-Day Decisions

Use angle relationships to interpret the team's plans. Show your reasoning on scratch paper.

11.

On Priya's launch-rail plan, the vertical reference line is perpendicular to the level ground. The rail lies between them, making an angle of (x + 2)° with the vertical and (9x + 8)° with the ground.

What angle does the rail make with the ground? °

12.

Malik draws two straight sight lines crossing on the tracking display. One pair of vertical angles is labeled (4x + 14)° and (6x − 20)°. The team needs the measure of an angle that forms a linear pair with either labeled angle. A linear pair consists of adjacent angles whose other sides form a straight line.

What measure should the team record? °

13.

A folding equipment stand has two adjacent angles that form a straight angle. The angles measure (5x + 10)° and (3x + 26)°. The design passes inspection only if the larger angle is at least 95°. Which conclusion is correct?

A. The design passes because the larger angle is 110°.B. The design fails because the larger angle is 90°.C. The design fails because the larger angle is 80°.D. The design passes because the larger angle is 100°.

14.

Elena divides a 126° viewing angle into two adjacent angles measuring 42° and (3x + 6)°. She writes 42 + (3x + 6) = 90 because the angles are adjacent. Explain her error, write the correct equation, and find x.