Question

THE MEASURE OF ANGLES OF A TRIANGLE ARE IN RATIO OF 5:6:7.THEN THE MEASURE OF THE GREATEST ANGLE IS ​

Answer 1

Answer:

Here is your answer FRIEND

The measure of the greatest angle is 70°

Step-by-step explanation:

Let the measure = x

So, 5:6:7 = 5x, 6x and 7x

Sum of triangle = 180°

So, 5x + 6x + 7x = 180°

18x = 180°

Therefore, x = 180/18 = 10°

This means that :

5x = 5 × 10 = 50°

6x = 6 × 10 = 60° and

7x = 7 × 10 = 70°

So the measure of the greatest angle is 70°

HOPE IT HELPS

HAVE A GREAT DAY FRIEND

Answer 2

$\large\underline{\sf{Solution-}}$

$\large\underline{\sf{Solution-}}$

Given that,

• The measure of angles of a triangle are in the ratio 5 : 6 : 7.

Let assumed that,

$\begin{gathered}\begin{gathered}\bf\: Angles \: be \: \begin{cases} &\sf{5x} \\ \\ &\sf{6x} \\ \\ &\sf{7x} \end{cases}\end{gathered}\end{gathered}$

We know,

Sum of interior angles of a triangle is supplementary.

So,

$\rm :\longmapsto\:5x + 6x + 7x = 180$

$\rm :\longmapsto\:18x = 180$

$\bf\implies \:x = 10$

So,

$\begin{gathered}\begin{gathered}\bf\: Angles \: aee \: \begin{cases} &\sf{5x = 5 \times 10 = 50} \\ \\ &\sf{6x = 6 \times 10 = 60} \\ \\ &\sf{7x = 7 \times 10 = 70} \end{cases}\end{gathered}\end{gathered}$

• Thus, Greatest angle is 70°.

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Properties of a triangle

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

Sum of interior angles of a triangle is supplementary.

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

The side opposite to the greater angle of a triangle is the longest side.

Angle opposite to longest side is always.

Exterior angle of a triangle is equals to sum of interior opposite angles.