Question

The ratio of the measures of the angles of a triangle is 3:8:9. Find the measure of each angle.

Answer 1

Answer:

Let the three angles be 3x, 8x and 9x

As we know that each triangle constitutes of 180°

so ATQ,

3x+8x+9x = 180°

20x = 180°

x=9°

.

.

Now substitute the value of x=9° in 3x, 8x and 9x

.

3x = 3(9) = 27°

8x = 8(9) = 72°

9x = 9(9) = 81°

.

Hence these are your values.

Answer 2

Given:

The ratio of the measures of the angles of a triangle is "3:8:9".

To Find:

The measure of each angle.

Solution:

$\sf{\underline{★According \:to\:the\: question:}}$

The ratio of measures of angle are 3:8:9

➺so now let the angles be 3x,8x,9x

$\sf {\underbrace{ \pink{sum \: of \: interior \: angles \: in \: a \: triangle \: is \: 180° }}}$

$⇒\tt {\: now \: the \: sum \:of \: angles = 180°} \\ \\ \\ \sf : ⟹ 3x + 8x + 9x = 180° \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf: ⟹ 20x = 180° \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf: ⟹ x = \cancel \frac{180}{20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf: ⟹ x = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, now the angles are

$\sf3x = 3(9) = \pink{ 27°} \\ \sf \: 9x = 9(9) = \blue{ 81°} \: \\ \sf \: 8x = 8(9) = \orange{72°}$

$\blue{ \underline{ \boxed{ \mathfrak{ \purple{ \therefore \: the \: angles \: are \: 27,81,72}}}}}$

Verification:-

To check weather we are right let's add up the numbers and check weather they make 180°

$\sf\pink{let's start:}$

$⟼27 + 81 + 72 = 180 \\ \\ ⟼108 + 72 = 180 \: \: \: \: \: \: \\ \\ ⟼180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf l.h.s = r.h.s \\ \\ \mathfrak { \huge{ \purple{ \dag{hence \: verified}}}}$

hope this helps.!!