**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.

**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".

Apart from the stuff given above, if you want to know more about "Solving equations that represent geometric concepts", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**