Question

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. Find the measure of each angle.
​

Answer 1

Required Answer :

• Angle A = 90°
• Angle B = 40°
• Angle C = 50°

STEP BY STEP EXPLANATION :

Given :

in ∆ ABC ,

• angle A = Angle B + Angle C

• Angle B and C ratio = 4:5

To Find :

• Measure of all angles of triangle.

Explanation :

Let the Angle B = 4x

nd,Angle C = 5x

hence, by the Given question Angle A = 4x + 5x

so, Measure of Angle A = 9x

. According to a property of triangle :-

• Sum of interior angle of triangle is always 180°

So, by using this property, we can find our required answer as :

$by \: using \: a \: property \: of \: triangle \: given \: above \:$

Angle A + Angle B+ Angle C = 180°

=> 9x + 4x + 5x = 180°

=> 18x = 180°

=> x = 180/18

=> x 10°

hence, we found Value of x by Explanation given above .

Now,

Finding the measurement of all angles of triangle by putting the value of x :-

• Angle A =

9x = 9 × 10 = 90°

• Angle B =

4x = 4× 10 = 40°

• Angle C =

5x = 5 × 10 = 50°

Hence,

Three angles are as =>

• Angle A = 90°
• Angle B = 40°
• Angle C = 50°

Verifying :

• Given that the Measure of Angle A is = Measure of Angle B + Angle C

so here ,

We have to verify that :-

Angle A = Angles B + Angle C

=> 90° = 40° + 50°

=> 90° = 90°

LHS = RSH

Hence verified

Answer 2

Step-by-step explanation:

Required Answer :

Angle A = 90°

Angle B = 40°

Angle C = 50°

STEP BY STEP EXPLANATION :

Given :

in ∆ ABC ,

angle A = Angle B + Angle C

Angle B and C ratio = 4:5

To Find :

Measure of all angles of triangle.

Explanation :

Let the Angle B = 4x

nd,Angle C = 5x

hence, by the Given question Angle A = 4x + 5x

so, Measure of Angle A = 9x

. According to a property of triangle :-

Sum of interior angle of triangle is always 180°

So, by using this property, we can find our required answer as :

by using a property of triangle given above

Angle A + Angle B+ Angle C = 180°

=> 9x + 4x + 5x = 180°

=> 18x = 180°

=> x = 180/18

=> x 10°

hence, we found Value of x by Explanation given above .

Now,

Finding the measurement of all angles of triangle by putting the value of x :-

Angle A =

9x = 9 × 10 = 90°

Angle B =

4x = 4× 10 = 40°

Angle C =

5x = 5 × 10 = 50°

Hence,

Three angles are as =>

Angle A = 90°

Angle B = 40°

Angle C = 50°

Verifying :

Given that the Measure of Angle A is = Measure of Angle B + Angle C

so here ,

We have to verify that :-

Angle A = Angles B + Angle C

=> 90° = 40° + 50°

=> 90° = 90°

LHS = RHS

Hence verified ✅✅✅✅✅✅✅✅