Question

Angle ACD is supplementary to angles ACE and BCD and congruent to angle BCE.

2 lines intersect. Lines D E and A B intersect at point C.
Which statements are true about the angles in the diagram? Select three options.

Angle ACE is supplementary to angle BCD.
Angle BCE is supplementary to angle ACE.
Angle BCD is supplementary to angle BCE.
Angle ACE is congruent to angle BCE.
Angle BCD is congruent to angle ACE

Answer 1

Answer:

Step-by-step explanation:

Angle BCE is supplementary to angle ACE.

Angle BCD is supplementary to angle BCE.

Angle BCD is congruent to angle ACE

Answer 2

Angles are said to be supplementary, if they add up to $180^o$, while congruent angles are equal.

The true statements are:

(b) Angle BCE is supplementary to angle ACE.

(c) Angle BCD is supplementary to angle BCE.  

(e) Angle BCD is congruent to angle ACE

Analyzing the options.

(a) $\angle ACE$ and $\angle BCD$ are supplementary

From the attached figure, $\angle ACE$ and $\angle BCD$ are congruent because they are corresponding angles

i.e.

$\angle ACE = \angle BCD$

Hence, (a) is false.

(b) $\angle BCE$ and $\angle ACE$ are supplementary

From the attached figure, $\angle BCE$ and $\angle ACE$ are supplementary because they add up to $180^o$

i.e.

$\angle BCE + \angle ACE = 180^o$

Hence, (b) is true.

(c) $\angle BCD$ and $\angle BCE$ are supplementary

From the attached figure, $\angle BCD$ and $\angle BCE$ are supplementary because they add up to $180^o$

i.e.

$\angle BCD + \angle BCE = 180^o$

Hence, (c) is true.

(d) $\angle ACE$ and $\angle BCE$ are congruent

From the attached figure, $\angle ACE$ and $\angle BCE$ are not congruent, but rather they are supplementary because they add up to $180^o$

i.e.

$\angle BCE + \angle ACE = 180^o$

and

$\angle BCE \ne \angle ACE$

Hence, (d) is false.

(e) $\angle BCD$ and $\angle ACE$ are congruent

As stated in (a), that:

$\angle ACE = \angle BCD$

This means that they are congruent.

Hence, (e) is true.

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