Using Equations to Solve for Unknown Angles

Multiple Choice

Segments (AB), (DC), and (EC) intersect at point (C). Angle (DCE) measures ( $$148^{\circ}$$ ). Find the value of (x).

• 12
• 45
• 60
• 32

Multiple Choice

Line $$\ell$$ is perpendicular to line $$m$$ . If $$w = 138^\circ$$ , find the value of $$x$$ .

• 45
• 90
• 117
• 23

Multiple Choice

Line $$\ell$$ is perpendicular to line $$m$$ . What is the value of $$w$$ ?

• 90
• 42
• 60
• 30

Open Ended

If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.

Multiple Choice

What is the measurement of angle $$ABF$$ given that $$B$$ is the intersection of line $$AC$$ and line $$ED$$ ? Angle GBC measures 65 degrees, angle FBE measures 20 degrees, and angle ABE is labeled 110 degrees.

• 165 degrees
• 180 degrees
• 130 degrees
• 150 degrees

Multiple Choice

What is the measurement of angle $$ABD$$ given that $$B$$ is the intersection of line $$AC$$ and line $$ED$$ ? Two lines and two rays intersect at point B creating 6 angles. Line AC is slanted downward and to the right and line ED is slanted upward and to the right. Ray BG is drawn between line segment BD and line segment BC. Angle GBC that is formed measures 65 degrees. Ray BF is drawn between line segment BC and line segment BE. Angle FBE that is formed measures 20 degrees. Angle ABE is labeled 110 degrees.

• 165 degrees
• 90 degrees
• 180 degrees
• 150 degrees

Multiple Choice

What is the measurement of angle $$EBC$$ given that $$B$$ is the intersection of line $$AC$$ and line $$ED$$ ? Line AC is slanted downward and to the right and line ED is slanted upward and to the right. Ray BG is drawn between line segment BD and line segment BC. Angle GBC measures 65 degrees. Ray BF is drawn between line segment BC and line segment BE. Angle FBE measures 20 degrees. Angle ABE is labeled 110 degrees.

• 90 degrees
• 150 degrees
• 180 degrees
• 165 degrees

Multiple Choice

What is the measurement of angle $$FBC$$ given that $$B$$ is the intersection of line $$AC$$ and line $$ED$$ ? Line AC is slanted downward and to the right and line ED is slanted upward and to the right. Ray BG is drawn between line segment BD and line segment BC. Angle GBC measures 65 degrees. Ray BF is drawn between line segment BC and line segment BE. Angle FBE measures 20 degrees. Angle ABE is labeled 110 degrees.

• 165 degrees
• 180 degrees
• 150 degrees
• 90 degrees

Multiple Choice

What is the measurement of angle DBG given that B is the intersection of line AC and line ED, angle GBC measures 65 degrees, angle FBE measures 20 degrees, and angle ABE is labeled 110 degrees?

• 165 degrees
• 90 degrees
• 180 degrees
• 150 degrees