Question

Two angles are adjacent, as shown in the diagram below

Part A: Use complete sentences to describe the relationship between the adjacent angles. Be sure to include specific terms from the lesson.

Part B: Set up an equation and solve for x. In your answer, include the equation, your calculations and the value of x.

Part C: Use your equation from Part A and the value of x from Part B to prove your equation to be true for the adjacent angles in the diagram.

Answer 1

I don’t have the diagram or the algebraic expressions for the two angles. Could you either attach the diagram or tell me the algebraic expressions (or numeric measures) shown for each angle and whether the two angles form a straight line or a right angle? With that I can give the exact Part A–C answers.

Below I’ll give a clear template and one worked example you can follow or adapt once you provide the actual expressions.

Template (what to write for each Part)
- Part A (verbal description): Use a complete sentence that names the relationship. Example sentence forms:
- If the two adjacent angles form a straight line: “The two angles are adjacent and form a linear pair: they share a common vertex and one common side, and their other sides are opposite rays. Therefore the angles are supplementary, so their measures add to 180 degrees.”
- If they form a right angle (together 90°): “The two angles are adjacent and complementary: they share a vertex and a side and their measures add to 90 degrees.”
- If they are equal in measure and adjacent: “The two angles are adjacent and congruent: they share a vertex and side and have equal measures.”

- Part B (set up and solve): Write the appropriate equation using the relationship from Part A, then solve for x showing steps. For example:
- Supplementary case: if angle1 = expression A and angle2 = expression B, set A + B = 180, then show algebra steps to isolate x and state x = value.
- Complementary case: set A + B = 90 and solve.
- Congruent case: set A = B and solve.

- Part C (verify): Substitute the found x back into the original expressions, compute each angle measure, and show they satisfy the relationship (their sum equals 180 or 90, or they are equal).

Worked example (supplementary/linear-pair example)
- Suppose the diagram shows two adjacent angles that form a straight line and the measures are m∠1 = 3x + 15 and m∠2 = 2x + 30.

Part A (complete sentence)
The two angles are adjacent and form a linear pair: they share a vertex and a side and their noncommon sides are opposite rays, so the angles are supplementary and their measures add to 180 degrees.

Part B (equation and solve)
Set up the equation using the supplementary relationship:
(3x + 15) + (2x + 30) = 180
Combine like terms:
5x + 45 = 180
Subtract 45 from both sides:
5x = 135
Divide by 5:
x = 27

Part C (verify)
Substitute x = 27 back into the angle expressions:
m∠1 = 3(27) + 15 = 81 + 15 = 96
m∠2 = 2(27) + 30 = 54 + 30 = 84
Check the relationship: 96 + 84 = 180, so the equation (3x + 15) + (2x + 30) = 180 is true for these adjacent angles.

Send me the actual expressions or the picture and I’ll solve your specific problem the same way.