Question

8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°

Answer 1

Measurement of ∠CED is $52$° with the help of vertically opposite angles.

To find out the angle which is to be found first let's understand the vertically opposite angle first:

What are vertically opposite angles?

Vertically opposite angles are angles that are opposite each other at a particular vertex and are formed by two straight intersecting lines.

Vertically opposite angles are equal to each other.

They are sometimes called vertical angles.

When two lines intersect, the opposite angles formed as a result of the intersection are called vertical or vertically opposite angles. A pair of vertically opposite angles are always equal. Also, a vertical angle and its adjacent angle are always complementary, i.e. they add up to $180$ degrees. For example, if two lines intersect and form an angle, say X=$45$°, then its opposite angle is also equal to $45$°. And the angle adjacent to X will be equal to $180-45=35$°.

Now according to the question

∠BED=$90$°

And also ∠BED=∠BEC+∠CED

∠CED=∠BED-∠BEC

Hence ∠CED=$90$°-$38$$38$°

where ∠BEC and ∠AEF are vertically opposite angles.

Hence ∠CED=$52$°

Learn more about vertically opposite angles here:

brainly.com/question/18045519

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