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Figure NOT drawn to scale.
In the figure above, if the degree measure of a central angle subtending the red arc is \(100°\) and the degree measure of a central angle subtending the blue arc is \(210°\), then what is the value of \(x° - y°\) ?
A. \(110°\)
B. \(130°\)
C. \(145°\)
D. \(155°\)
E. \(165°\)
03 Dec 2021, 03:31
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Official Solution:
Figure NOT drawn to scale.
In the figure above, if the degree measure of a central angle subtending the red arc is \(100°\) and the degree measure of a central angle subtending the blue arc is \(210°\), then what is the value of \(x° - y°\) ?
A. \(110°\)
B. \(130°\)
C. \(145°\)
D. \(155°\)
E. \(165°\)
We need the following properties to solve this question:
An inscribed angle is exactly half the corresponding central angle.
Since the red arc is \(100°\), then inscribed angle that subtends this arc will be half of that, so \(50°\).
Since the blue arc is \(210°\), then inscribed angle that subtends this arc will be half of that, so \(105°\).
Check the image below:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
Since angle \(x\) is an exterior angle of the yellow triangle, then \(x=50+105=155°\).
The sum of angles that are formed on a straight line is equal to 180°.
Since angles \(x\) and \(y\) form a straight line, then \(x+y=180°\). So, \(y=180°-155°=25°\).
Finally, \(x° - y°=155°-25°=130°\).
Answer: B
Figure NOT drawn to scale.
In the figure above, if the degree measure of a central angle subtending the red arc is \(100°\) and the degree measure of a central angle subtending the blue arc is \(210°\), then what is the value of \(x° - y°\) ?
A. \(110°\)
B. \(130°\)
C. \(145°\)
D. \(155°\)
E. \(165°\)
We need the following properties to solve this question:
An inscribed angle is exactly half the corresponding central angle.
Since the red arc is \(100°\), then inscribed angle that subtends this arc will be half of that, so \(50°\).
Since the blue arc is \(210°\), then inscribed angle that subtends this arc will be half of that, so \(105°\).
Check the image below:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
Since angle \(x\) is an exterior angle of the yellow triangle, then \(x=50+105=155°\).
The sum of angles that are formed on a straight line is equal to 180°.
Since angles \(x\) and \(y\) form a straight line, then \(x+y=180°\). So, \(y=180°-155°=25°\).
Finally, \(x° - y°=155°-25°=130°\).
Answer: B
