Using Equations to Solve for Unknown Angles

Warmup

(1.) Notice when the sides of the angles are adjacent and the vertices meet at one point, they form a straight angle.

What is the measure of a straight angle?

(2.) Tyler thinks that the figure below has enough information to figure out the values of a and b.

Do you agree? Explain your reasoning.

Activity #1

Solve for Unknown Angles Between Intersecting Lines.

• Study each diagram below carefully and answer the questions that follow.

Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.

(2.) Now solve for the missing angles, x and w.

(4.) Now solve for the missing angle, w.

(6.) Now solve for the missing angles, w.

(8.) Now solve for the missing angles, w .

(10.) Now solve for the missing angles, w and x.

Activity #2

Find Unknown angles between Intersecting Lines.

• Study the diagrams below and find the missing angles.
• Show your thinking. Organize it so it can be followed by others. Geometric tools can be found under in the applet.

Activity #3

Find Unknown angles between Intersecting Lines.

The right half of the figure below is representing the different angles on the left. The two bold lines are parallel.

• Find the other 7 missing angle measures. When you enter a correct value (right side), this angle will appear in the diagram. Note: LARGE POINTS are moveable.
• When you find the 7 missing angles, click to get another set of angles.

Challenge #1

Find the value of X:

Challenge #2

The diagram below contains three squares. Three additional segments have been drawn that connect corners of the squares. We want to find the exact value of a + b + c.

Use a protractor to measure the three angles.

(1.) Use your measurements to conjecture about the value of a + b + c.

(2.) Find the value of a + b + c by reasoning about the diagram.

Quiz Time