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The angle A of a triangle ABC is equal to the sum of the other two angles . Also , the ratio of the angle B to the angle C is 4 : 5. Determine the three angles of the triangle ABC

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A = 90^{o}, B = 40^{o}, C = 50^{o}

A = 40^{o}, B = 40^{o}, C = 50^{o}

A = 50^{o}, B = 40^{o}, C = 50^{o}

A = 70^{o}, B = 40^{o}, C = 50^{o}

answer is A.

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Detailed Solution

Concept- Given that the ratio of angle B to angle

C is 4,

we can write the angles as

∠ B = 4 and ∠ C = 5 .

Given that angle A is equal to the total of the other two angles, we may calculate the angles using the formula

∠ A = 9 x

and the fact that the sum of all the angles in a triangle is 180.
An ABC triangle is presented to us.

The angle A is specified as being equal to the product of the angles B and C, or ∠A=∠B+∠C……….(1)
Next, we are informed that angle B:angle C is a 4:5 ratio.
Since the ratio is provided, we may express the angles as

∠ B = 4 x

and

∠ C = 5 x .

By applying this in (1), we have

∠ A = 4 x + 5 x ∠ A = 9 x .

By employing the triangle's angle sum property, we can determine
that the sum of a triangle's angles is 180.
We obtain,

x = \frac{180}{18} using the values found above : 9 x + 4 x + 5 x = 180 x = 180 .

We can calculate the angles

∠ A = 9 x = 9 (10) = 90

∠ B = 4 x = 4 (10) = 40

, and ∠C=5x=5(10)=50 using the value of x.
Hence, choice 1 is the best one.

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