Question

Name two pairs of complementary angles in the diagram.

Name two pairs of supplementary angles in the diagram.

Draw and label with its measure another angle to make a pair of vertical angles.

Answer 1

Step-by-step explanation:

Two pairs of complementary angle:-

( 62,28) (40,50)

Two pairs of supplementary angle:-

(125,55) (90,90)

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Answer 2

Tip:

Recall the definition of complementary and supplementary angles.

• Complementary angles are a pair of angles whose sum is $90^\circ$.

• Supplementary angles are a pair of angles whose sum is $180^\circ$.

Vertical angles are angles opposite to each other when two lines intersect each other.

Explanation:

1. In the given figure, check for pairs that add up to $90^\circ$

In $\triangle CED,$

$\angle CDE+\angle CED=90^\circ$

In $\triangle BAF,$

$\angle BAF+\angle BFA=90^\circ$

So the two pairs of complementary angles are $(\angle CDE,\angle CED),(\angle BAF,\angle BFA)$

2. In the given figure, check for pairs that add up to $180^\circ$

In quadrilateral $BCEF$

$\angle BFE+\angle FBC=180^\circ$

$\angle BCE+\angle CEF=180^\circ$

So the two pairs of complementary angles are $(\angle BFE,\angle FBC),(\angle BCE,\angle CEF)$

3. Refer to the attached figure,

$(\angle AOB,\angle DOC), (\angle AOD,\angle BOC)$ are pairs of vertical angles