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Find the m 33
43
57
67

Find the m 33 43 57 67-example-1
User Milevyo
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2 Answers

5 votes
What does the m stand for?
User RyuuGan
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7.4k points
4 votes

Answer: The correct option is

(A) 33°.

Step-by-step explanation: In the given figure, AB ║ CD and BC║ DE.

Also, m∠BCA = 90° and m∠BAC = 57°.

We are to find the measure of angle CDE.

We know that

the sum of the measures of the three angle of a triangle is 180°, so from triangle ABC, we have


m\angle BCA+m\angle BAC+m\angle ABC=180^\circ\\\\\Rightarrow 90^\circ+57^\circ+m\angle ABC=180^\circ\\\\\Rightarrow m\angle ABC=180^\circ-90^\circ-57^\circ\\\\\Rightarrow m\angle ABC=180^\circ-143^\circ\\\\\Rightarrow m\angle ABC=33^\circ.

Now, since AB ║ CD and BC is a transversal so we get


m\angle ABC=m\angle BCD~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Similarly, since BC║ DE and CD is the tranversal, so we get


m\angle BCD=m\angle CDE~[\textup{alternate interior angles}]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

From equations (i) and (ii), we get


m\angle CDE=m\angle ABC=33^\circ.

Thus, the required measure of angle CDE is 33°.

Option (A) is CORRECT.

User Jcgrowley
by
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