# ANGLE PAIRS AND ONE STEP EQUATIONS

## About "Angle pairs and one step equations"

Angle pairs and one step equations :

Vertical angles are the opposite angles formed by two intersecting lines. Vertical angles are congruent because the angles have the same measure.

Adjacent angles are pairs of angles that share a vertex and one side but do not overlap.

Complementary angles are two angles whose measures have a sum of 90°.

Supplementary angles are two angles whose measures have a sum of 180°. We discovered in the Explore Activity that adjacent angles formed by two intersecting lines are supplementary.

## Angle pairs and one step equations - Examples

Example 1 :

Look at the diagram given below and answer the question.

A. Name a pair of vertical angles :

Vertical angles are opposite angles formed by intersecting lines.

<AFB and <DFE are vertical angles.

B. Name a pair of adjacent angles :

Adjacent angles share a vertex and a side but do not overlap.

<AFB and <BFD are adjacent angles.

C. Name a pair of supplementary angles :

Adjacent angles formed by intersecting lines are supplementary.

<AFB and <BFD are supplementary angles.

D. Name two pairs of supplementary angles that include <DFE :

Any angle that forms a line with <DFE is a supplementary angle to <DFE.

<DFE and <EFA are supplementary angles, as are <DFE and <DFB.

E. Find the measure of angle <AFB :

Use the fact that <AFB and <BFD in the diagram are supplementary angles to find m<AFB.

<AFB + <BFD  =  180°

From the given diagram, we have <AFD  =  x and also m<BFD  =  50° + 90°  =  140°

x + 140°  =  180°

Subtract 140° from both sides.

(x + 140°) - 140°  =  180° - 140°

x  =  40°

The measure of m<AFB is 40°

Example 2 :

Find the value of  "x" in the diagram given below.

Solution :

From the picture above, it is very clear (x+7)° and 100° are vertical angles and also they are congruent.

So, we have

x + 7  =  100

Subtract 7 from both sides

(x + 7) - 7  =  100 - 7

x  =  93

Hence the value of "x" is 93.

After having gone through the stuff given above, we hope that the students would have understood "One step equations on angle pairs".

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