Decide which of the following is a reasonable answer for .

Mathematics

1 answer:

Nikolay [14]3 years ago

3 0

Follow for what REEEEE

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In the figure below, CD bisects m∠ACB, AB=BC, m∠BEC=90°, and m∠DCE=42°. Find the measure of ∠A.

vesna_86 [32]

Answer: ∠A= $24\textdegree$

Step-by-step explanation:

Since we have given that

CD bisects m∠ACB,

⇒ m∠ACD= m∠DCB =x (say)

And, AB=BC, m∠BEC=90°, and m∠DCE=42°

So,

m∠CAD=m∠ACD

In ΔDCE,

$\angle DCE+\angle CED+\angle CDE=180\textdegree\\\\(\text{Sum of anlges in triangle is }180\textdegree)\\\\42\textdegree+90\textdegree+\angle CDE=180\textdegree\\\\132\textdegree+\angle CDE=180\textdegree\\\\\angle CDE=180\textdegree-132\textdegree\\\\+\angle CDE=48\textdegree$