Answer:
x° = 36°
Explanation:
You want to find the angle between a secant and a tangent to a circle, where the intercepted arcs are 126° and 54°.
Exterior angle
The angle at D, labeled x°, is half the difference of the intercepted arcs:
x° = (126° -54°)/2 = 72°/2
x° = 36°
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Additional comment
The same relationship applies for the angle between two secants.
This is easy to prove by considering triangle ADE. Angle DAE is half of arc CE. The exterior angle to the triangle at E is half of arc AE. That exterior angle is equal to the sum of the remote interior angles at D and A:
AE/2 = x° + CE/2 ⇒ x° = (AE -CE)/2