The vertex of an angle measuring 32° is in the exterior of a circle and its sides are secants of the circle. If the sum of the measures of the intercepted arcs is 180°, find the measure of each intercepted arc.
Please Ask with two measurements
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Given: Vertex of an angle measuring 32°, sum of the measures of the intercepted arcs is 180°.
To find: Measure of each intercepted arc.
Solution:
- Now we have given that the vertex of an angle measuring 32° is in the exterior of a circle and its sides are secants of the circle.
- So, the value of the outer angle is the semi-difference of the arcs.
- Let x and y be the intercepts arcs.
- Now:
x + y = 180° ..............(i)
- According to the question:
32° = 1/2 ( x - y )
64° = x - y ...............(ii)
- Now solving (i) and (ii) simultaneously, we get:
2x = 244°
x = 122°
- Putting x = 122° in (ii), we get:
64° = 122 - y
y = 122° - 64°
y = 58°
Answer:
So, the measures of the intercepts arcs y and x are 58° and 122° respectively.
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Answer:58 and 122
Step-by-step explanation:
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