SOLVING EQUATIONS THAT REPRESENT GEOMETRIC CONCEPTS

About "Solving equations that represent geometric concepts"

Solving equations that represent geometric concepts :

We can represent geometric relationships using equations.

Recall that a straight line has an angle measure of 180°. Two angles whose measures have a sum of 180° are called supplementary angles.

Two angles whose measures have a sum of 90° are called complementary angles.

Solving equations that represent geometric concepts - Examples

Example 1 :

Find the measure of the unknown angle in the figure given below. Solution :

Step 1 :

Write a word equation based on the situation.

In the given figure, the unknown angle "x" and the given angle 60° form angle on the straight line.

We know that the angle on the straight line measures 180°.

So, we have Step 2 :

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

x + 60°  =  180°

(x represents the measure of the unknown angle in degrees)

Step 3 :

Solve the equation : x + 60°  =  180°

Since we are trying to solve for "x", we have to get rid of 60° which is added to "x".

To get rid of 60°, we have to subtract 60° on both sides.

(x + 60°) - 60°  =  (180°) - 60°

x  =  120°

Hence, the unknown angle is 120°.

Example 2 :

Find the measure of the unknown angle in the figure given below. Solution :

Step 1 :

Write a word equation based on the situation.

In the given figure, the unknown angle "x" and the given angle 65° form right angle.

We know that the right angle measures 90°.

So, we have Step 2 :

Rewrite the equation using a variable for the unknown quantity and the given values for the known quantities.

x + 65°  =  90°

(x represents the measure of the unknown angle in degrees)

Step 3 :

Solve the equation : x + 65°  =  90°

Since we are trying to solve for "x", we have to get rid of 65° which is added to "x".

To get rid of 65°, we have to subtract 65° on both sides.

(x + 65°) - 65°  =  (90°) - 65°

x  =  25°

Hence, the unknown angle is 25°.

After having gone through the stuff given above, we hope that the students would have understood "How to solve equations that represent geometric concepts".

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