Prove that each exterior angle of a triangle is equal to the sum of the interior opposite angles - Junior Cycle Mathematics - Question 12 - 2019
Question 12
Prove that each exterior angle of a triangle is equal to the sum of the interior opposite angles.
Diagram:
Given:
Triangle with angles labelled A, B, C and D
To P... show full transcript
Worked Solution & Example Answer:Prove that each exterior angle of a triangle is equal to the sum of the interior opposite angles - Junior Cycle Mathematics - Question 12 - 2019
Step 1
Diagram:
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Answer
Draw triangle ABC with exterior angle D at vertex C, ensuring all angles are labelled correctly.
Step 2
Proof:
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Answer
|∠A| + |∠B| + |∠C| = 180°
Reason: Angles in a triangle sum to 180°.
Step 3
Step 3:
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Answer
|∠C| + |∠D| = 180°
Reason: Angles on a straight line sum to 180°.
Step 4
Step 4:
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Answer
Subtracting |∠C| from both sides gives:
|∠D| = |∠A| + |∠B|
Thus, each exterior angle (|∠D|) is equal to the sum of the interior opposite angles (|∠A| + |∠B|).
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