A student is solving for the unknown angle in a supplementary pair. The two angles are $$(7x + 5)°$$ and $$(3x - 15)°$$ . The student sets up the equation as $$7x + 5 + 3x - 15 = 90$$ and gets $$x = 10$$ . Identify the error and find the correct value of $$x$$ .

The student used the wrong sum; the correct equation is $$7x + 5 + 3x - 15 = 180$$ , giving $$x = 19$$

The student made an arithmetic error; the correct value is $$x = 10$$

The student used the wrong sum; the correct equation is $$7x + 5 - (3x - 15) = 180$$ , giving $$x = 40$$

The student set up the equation correctly; supplementary angles sum to $$90°$$

Two angles are formed along a straight road where a smaller path branches off. The angles on one side of the path measure $$(5x + 10)°$$ and $$(3x + 14)°$$ and together they form a straight line. A student claims both angles are complementary. Analyze the student's claim and determine the correct angle measures.

The student is incorrect; the angles are supplementary, measuring $$100°$$ and $$80°$$

The student is correct; both angles sum to $$90°$$ and each measures $$45°$$

The student is incorrect; the angles are supplementary, measuring $$85°$$ and $$95°$$

The student is incorrect; the angles are supplementary, measuring $$95°$$ and $$85°$$

A student claims that if two angles are both supplementary to the same angle, then the two angles must be equal to each other. Is this claim correct? Justify your reasoning by selecting the best answer.

Yes, because if $$\angle A + \angle C = 180°$$ and $$\angle B + \angle C = 180°$$ , then $$\angle A = \angle B$$

No, because supplementary angles can have any measures as long as they sum to $$180°$$

Yes, because both angles would each equal $$90°$$

No, because supplementary angles must be adjacent

Which of the following correctly identifies a pair of vertical angles?

Two non-adjacent angles formed by two intersecting lines that are opposite each other

Two angles that share a common side and a common vertex

Two angles whose measures add up to $$180°$$

Two angles that together form a right angle

Two intersecting lines form four angles. Angle 1 measures $$(3x + 5)°$$ , and Angle 2 is adjacent to Angle 1. Angle 3 is vertical to Angle 1, and Angle 4 is vertical to Angle 2. If Angle 1 and Angle 2 are supplementary and Angle 1 measures $$110°$$ , what are the measures of all four angles?

Angle 1 = $$110°$$ , Angle 2 = $$70°$$ , Angle 3 = $$110°$$ , Angle 4 = $$70°$$

Angle 1 = $$110°$$ , Angle 2 = $$70°$$ , Angle 3 = $$70°$$ , Angle 4 = $$110°$$

Angle 1 = $$110°$$ , Angle 2 = $$110°$$ , Angle 3 = $$70°$$ , Angle 4 = $$70°$$

Angle 1 = $$110°$$ , Angle 2 = $$70°$$ , Angle 3 = $$70°$$ , Angle 4 = $$70°$$

A ramp is built against a wall. The angle between the ramp and the ground is $$(x + 15)°$$ , and the angle between the ramp and the wall is complementary to it. A builder incorrectly states that the angle between the ramp and the wall is $$(x + 75)°$$ because complementary angles differ by $$75°$$ . What is the correct expression for the angle between the ramp and the wall, and what is the error in the builder's reasoning?

The correct expression is $$(75 - x)°$$ ; the builder added instead of subtracting from $$90°$$

The correct expression is $$(75 - x)°$$ ; the builder confused complementary with supplementary angles

The correct expression is $$(x + 75)°$$ ; the builder is correct

The correct expression is $$(180 - x - 15)°$$ ; the builder used the wrong total

At a traffic intersection, two roads cross forming two pairs of vertical angles. A city engineer labels three of the four angles as $$\angle 1 = (8x - 10)°$$ , $$\angle 2 = (5x + 20)°$$ , and $$\angle 3$$ which is vertical to $$\angle 2$$ . Using angle relationships, determine the measure of $$\angle 3$$ and explain which relationship was used to find it.

$$\angle 3 = 110°$$ ; vertical angles are equal, so $$\angle 3 = \angle 2$$

$$\angle 3 = 130°$$ ; supplementary angles were used to find $$\angle 2$$ first

$$\angle 3 = 120°$$ ; $$\angle 3$$ is supplementary to $$\angle 1$$

$$\angle 3 = 110°$$ ; $$\angle 3$$ is supplementary to $$\angle 1$$ and adjacent to $$\angle 2$$

Angle Relationships in Real Life (8.MG.1ab)

Authored by Allison Cabral

Mathematics

8th Grade

CCSS covered

Angle Relationships in Real Life (8.MG.1ab)

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following best describes two angles that are supplementary?

Two angles that share a common vertex and a common side

Two angles that are across from each other when two lines intersect

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following correctly defines complementary angles?

Two angles that are formed opposite each other at an intersection

Two angles that share only a common vertex

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

CCSS.7.G.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A student says that two adjacent angles are always supplementary. Which of the following is a counterexample that proves the student wrong?

Tags

CCSS.7.G.B.5

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