From the diagram below write down three angles which together add up to 180° - Junior Cycle Mathematics - Question 10 - 2014
Question 10
From the diagram below write down three angles which together add up to 180°.
A, B, C since the three angles inside a triangle always add up to 180°.
From the diag... show full transcript
Worked Solution & Example Answer:From the diagram below write down three angles which together add up to 180° - Junior Cycle Mathematics - Question 10 - 2014
Step 1
From the diagram below write down three angles which together add up to 180°.
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Answer
The angles are |∠A|, |∠B|, and |∠C|. They satisfy the equation:
∣∠A∣+∣∠B∣+∣∠C∣=180°
Step 2
From the diagram above write down two angles which together add up to 180°.
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Answer
The angles are |∠C| and |∠D|. This is because they are supplementary angles that lie on a straight line, leading to the equation:
∣∠C∣+∣∠D∣=180°
Step 3
What can you conclude from your two statements about the relationship between |∠D| and (|∠A| + |∠B|)?
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Answer
From the first part, we have:
∣∠A∣+∣∠B∣+∣∠C∣=180°
And from the second part:
∣∠C∣+∣∠D∣=180°
Setting these two equations equal gives:
|∠A| + |∠B| = |∠D|$$
Therefore, we conclude that the sum of angles |∠A| and |∠B| is equal to angle |∠D|.
Step 4
Find the value of x in the diagram.
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Answer
From part (iii), we know that:
47°+x°=112°
Solving for x gives:
x°=112°−47°=65°
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