The points A, B, C, and D are shown on the diagram - Junior Cycle Mathematics - Question 7 - 2016
Question 7
The points A, B, C, and D are shown on the diagram. They are all on the circle k.
$|AB| = |AD|$ and $|BC| = |DC|$, as shown.
The sizes of some of the angles are mar... show full transcript
Worked Solution & Example Answer:The points A, B, C, and D are shown on the diagram - Junior Cycle Mathematics - Question 7 - 2016
Step 1
Calculate the value of x.
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Answer
To find the value of x, we utilize the property that the sum of angles in a cyclic quadrilateral is 180 degrees:
x+100°+(180°−x)+y=360°
This implies:
x+100°+180°−x+y=360°
Simplifying this gives:
y+280°=360°
Solving for x leads us to:
x=180°−100°=80°.
Thus, we find that:
x=80°.
Step 2
Calculate the value of y. Show all of your working out.
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Answer
From earlier calculations, we know:
y=180°−2(100°+80°)
This indicates:
y=180°−2180°y=180°−90°y=90°.
Thus, we conclude that:
y=90°.
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