**Problem 1 :**

Identify the type of triangle whose diagram is given below.

**Problem 2 :**

Identify the type of triangle whose diagram is given below.

**Problem 3 :**

Identify the type of triangle whose diagram is given below.

**Problem 4 :**

Identify the type of triangle whose diagram is given below.

**Problem 5 :**

If (2x + 15)°, (3x)° and (6x)° are the angles of a triangle, identify the type of triangle.

**Problem 1 :**

Identify the type of triangle whose diagram is given below.

**Solution :**

Let us consider the following two important points related to the given information.

(i) All the given three angles are different.

(ii) Each of the three angles is less than 90°

So, the given triangle is a scalene and acute triangle.

**Problem 2 :**

Identify the type of triangle whose diagram is given below.

**Solution :**

Let us consider the following two important points related to the given information.

(i) One of the angles is greater than 90°

(ii) Two sides are equal in length. The angles formed by the two congruent sides with the third side also must be equal.

So, the given triangle is an isosceles and obtuse triangle.

**Problem 3 :**

Identify the type of triangle whose diagram is given below.

**Solution :**

In the triangle above, the lengths of all the three sides are same and all the three angles are congruent.

So, the given triangle is equiangular triangle.

**Problem 4 :**

Identify the type of triangle whose diagram is given below.

**Solution :**

In the triangle above, two sides are congruent. The angles formed by the third side with two congruent sides will always be equal.

The diagram given below illustrates this.

By Triangle Sum theorem, we have

x + x + 40° = 180°

2x + 40° = 180°

Subtract 40° from both sides.

2x = 140°

Divide both sides by 2.

x = 70°

The angles measures of the given triangle are 40°, 70° and 70°.

Let us consider the following two important points from the above calculation.

(i) Two of the angles are equal

(ii) Each of the three angles is less than 90°.

From the above two points, we have

The given triangle is an isosceles and acute triangle.

**Problem 5 :**

If (2x + 15)°, (3x)° and (6x)° are the angles of a triangle, identify the type of triangle.

**Solution:**

The angle sum property of a triangle states that the angles of a triangle always add up to 180°.

Then,

(2x + 15)° + (3x)° + (6x)° = 180°

2x + 15 + 3x + 6x = 180

Simplify.

11x + 15 = 180

Subtract 15 from each side.

11x = 165

Divide each side by 11.

x = 15

Substitute 15 for x into the given expressions to find the angles of the triangle.

First angle = 2x + 15 = 2(15) + 15 = 45°

Second angle = 3x = 3(15) = 45°

Third angle = 6x = 6(15) = 90°

Let us consider the following two important points from the above calculation.

(i) Two of the angles are equal

(ii) One of the angles is 90°

So, the given triangle is an isosceles and right triangle.

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

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**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**

**Trigonometry 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**