**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.

**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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