Respuesta :

Answer:

The measure of  angle x is 90°

Step-by-step explanation:

Given the figure in which

∠1=88°, ∠6=89°

we have to find the value of x.

∠5=∠6=89°   (∵ Vertically opposite angles)

∠1+∠4=∠6  ( ∵ By exterior angle property)

88°+∠4=89°

∠4=89°-88°=1°

As AC=CB (both are radii of same circle)

∴ ∠4=∠3=1°

Now, by exterior angle property

x=∠5+∠3=89°+1°=90°

Hence, the measure of  angle x is 90°

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akposevictor

Applying the angle of intersecting chords theorem, the value of x in the diagram showing the circle is: C. 90.

What is the Angle of Intersecting Chords Theorem?

According to the angle of intersecting chords theorem, the measure of the angle formed at the point of intersection of two chords inside a circle equals half the sum of the intercepted arcs.

89 = 1/2(88 + x) [based on the angle of intersecting chords theorem]

2(89) = 88 + x

178 = 88 + x

178 - 88 = x

x = 90° (Option C).

Learn more about the angle of intersecting chords theorem on:

https://brainly.com/question/2408975

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