Question

The angles of a triangle are in ratio 4:3:2. Find the measure of each of these angle​

Answer 1

Answer:

the answer is 80⁰,60⁰&40⁰.

Answer 2

$\large\underline{\bold{Given \:Question - }}$

• The angles of a triangle are in ratio 4:3:2. Find the measure of each of these angle.

$\large\underline{\bold{ANSWER-}}$

It is given that

• Angles of a triangle are in the ratio 4 : 3 : 2,

So,

$\begin{gathered}\begin{gathered}\bf \:Let \: the \: angles \: be - \begin{cases} &\sf{4x} \\ &\sf{3x}\\ &\sf{2x} \end{cases}\end{gathered}\end{gathered}$

We know,

• Sum of the angles of a triangle is 180°

So,

$\rm :\implies\:4x + 3x + 2x = 180 \degree \:$

$\rm :\longmapsto\:9x = 180\degree \:$

$\rm :\longmapsto\:x = 20\degree \:$

$\begin{gathered}\begin{gathered}\bf \:Hence, \: the \: angles \: be - \begin{cases} &\sf{4x \: = 4 \times 20 = 80\degree \:} \\ &\sf{3x = 3 \times 20 = 60\degree \:}\\ &\sf{2x = 2 \times 20 = 40\degree \:} \end{cases}\end{gathered}\end{gathered}$

Additional Information :-

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.