Question

one angle of a trangle is equal to the sum of the other two . if the ratio of the two angle is 7:8 find the angle of a trangle
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Answer 1

Given :

• One angle of a trangle is equal to the sum of the other two.

• The ratio of the two angle is 7:8.

To find :

• All the angle of a trangle =?

Step-by-step explanation :

Let the ratio of two angles of traingle are 7x and 8x.

It is Given that :

One angle of triangle is equal to the sum of the other two angles.

So,

7x + 8x = 15x.

Now,

We know that,

∠A + ∠B + ∠C = 180°

Substituting the values, we get,

7x + 8x + 15x = 180

30x = 180

x = 180/30

x = 6

Therefore, We know that value of x = 6° .

Hence,

∠A of traingle = 7x = 7 x 6 = 42°

∠B of triangle = 8x = 8 × 6 = 48°

∠C of traingle = 15x = 15× 6 = 90°

Answer 2

Answer:

Given information –

• Measure of one angle in a triangle is equal to the sum of the other two.
• The ratio of the measure of other two angles is 7:8.

To Find –

• Measure of all the angles of the triangle.

Solution –

Let assume the measure of two angles given as 7x and 8x.

According to the question, the sum of measure of the angles given is the measure of the third angle.

➸ 7x + 8x

➸ 15x

Hence, the measure of the third angle is 15x.

Now, We know that all the angles of the triangle sum to 180°.

➸ 15x + 7x + 8x = 180°

➸ 15x + 15x = 180°

➸ 30x = 180°

➸ x = 180/30

➸ x = 6

Hence, the value of x is 6°.

Value of the angles :

➸ 7x = 7*6 = 42°.

➸ 8x = 8*6 = 48°.

➸ 15x = 15*6 = 90°.

Hence, the measure of the angles of the triangle is 42°, 48° and 90°.