Question

If the angles of a triangle are in the ratio 2:13 the find the measure of smallest angle is

Answer 1

Step-by-step explanation:

We have angles of the triangle are in ratio 2 : 1 : 3

Let, the three angles of a triangle be 2k, 1k, 3k

We know that, Sum of all angles of a triangle is 180°.

2k + 1k + 3k = 180°

6k = 180°

k = 180/6

k = 30°

smallest angle = k = 30°

HENCE THE MEASURE OF THE SMALLEST ANGLE IS 30

UR QUESTION IS WRONG THE MEASURE IS 1:2;3

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Answer 2

Appropriate Question -

• If the angles of a triangle are in the ratio 2 :1 : 3. Find the measure of the smallest angle.

Answer -

• The measure of the smallest angle is 30°.

To find -

• The measure of the smallest angle.

Step-by-step explanation -

• Here, it is given that the angles of a triangle are in the ratio 2 : 1 : 3. We have to find the measure of the smallest angle.

Let :-

• The angles of the triangle be 2x, 1x and 3x.

We know that :-

$\underline{\boxed{\sf Sum \: of \: all \: the \: angles_{(triangle)} = 180^{\circ}}}$

Therefore,

$\longrightarrow \rm{2x + 1x + 3x = 180}$

$\longrightarrow \rm{6x = 180}$

$\longrightarrow \rm{x = \cancel{ \dfrac{180}{6}}}$

$\longrightarrow \rm{x = 30^{\circ}}$

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Hence, the angles are :-

$\bf 2x = 2 × 30 = 60^{\circ}$

$\bf 1x = 1 × 30 = 30^{\circ}$

$\bf 3x = 3 × 30 = 90^{\circ}$

We see that :-

• Here, the smallest number is 30.

Hence :-

• The measure of the smallest angle is 30°.

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