Use a Straight Angle to Find a Missing Angle
Two adjacent angles whose outside rays form a straight line make a linear pair.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: Two adjacent angles form a straight angle. One is 40°. Find the other. Candidate answers: (A) 140 ° (B) 180 ° (C) 40 ° (D) 50 °.
- Independent check inputs: Two adjacent angles form a straight angle. One is 43°. Find the other. Candidate answers: (A) 137 ° (B) 180 ° (C) 43 ° (D) 47 °.
Learn the idea
A scale drawing links represented and actual lengths through a fixed factor. Geometric relationships connect angles through straight lines and triangles, so a justified equation can replace guessing from a sketch. Two adjacent angles whose outside rays form a straight line make a linear pair. Their measures add to 180 degrees, allowing one to be recovered by subtraction.
Here is the method on the supplied teaching case. A straight angle totals 180°. Subtract the known angle: 180−40=140°. Adjacency alone would not imply supplementary angles.
Adjacent angles need not be supplementary unless their outer rays form a straight line. State that geometric condition before applying 180; a right angle instead supplies a 90-degree total.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: Two adjacent angles form a straight angle. One is 40°. Find the other. Candidate answers: (A) 140 ° (B) 180 ° (C) 40 ° (D) 50 °. Solution: A straight angle totals 180°. Subtract the known angle: 180−40=140°. Adjacency alone would not imply supplementary angles. The final answer is 140 °. Adjacent angles need not be supplementary unless their outer rays form a straight line. State that geometric condition before applying 180; a right angle instead supplies a 90-degree total.
Check your reasoning
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Helpful tips
- Two adjacent angles whose outside rays form a straight line make a linear pair.
- Adjacent angles need not be supplementary unless their outer rays form a straight line.
See the answer and explanation
137 °
A straight angle totals 180°. Subtract the known angle: 180−43=137°. Adjacency alone would not imply supplementary angles.
Take it further
Changed-input task: Two adjacent angles form a straight angle. One is 61°. Find the other. Candidate answers: (A) 119 ° (B) 180 ° (C) 29 ° (D) 61 °. Show the mathematical reason, not only the selected answer. Expected result: 119 °. A straight angle totals 180°. Subtract the known angle: 180−61=119°. Adjacency alone would not imply supplementary angles.
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