2 Answers

Richard Bos · Answer 1 · 2024-05-10T08:53:01+0000

Answer:

52°

Explanation:

The angle between two secants drawn from the point outside the circle is half the difference of the intercepted arcs.

$\sf \boxed{\bf \angle \ Y =(far \ arc - near \ arc)/(2)}$

$\sf \angle Y = \frac{m\overset{\frown}{GK} - m\overset{\frown}{CE}}{2}\\\\50 = \frac{152-m\overset{\frown}{CE}}{2}$

$50*2 = 152 - m\overset{\frown}{CE}\\\\100 = 152 - m\overset{\frown}{CE}$

$100 + m\overset{\frown}{CE} = 152\\\\$

$\sf m\overset{\frown}{CE}= 152 - 100\\\\m\overset{\frown}{CE} = 52^\circ$

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