Question

Find the measure of B and C​

Answer 1

Step-by-step explanation:

Let the common multiple be x

B=3x

C=2x

120=3x+2x ..........(Exterior Angle property)

120=5x

24=x

B=3x=3(24)=72°

C=2x=2(24)=48°

Hope it helps

Answer 2

Question :

In figure , ∠B : ∠C = 3 : 2 , BA is produced to D such that ∠CAD = 120°. Find the measures of ∠B and ∠C.

Given :

• Measure of ∠A = 120°

• Ratio of ∠B and ∠C = 3 : 2

To Find :

The measure of ∠B and ∠C.

Solution :

Let the ∠B and ∠C be 3x and 2x , respectively.

We know that , the sum of two co-interior angle is equal to one exterior angle.

Here the two co-interior angles as ∠B and ∠C and the exterior angle is ∠A , so the equation formed is :

$\underline{\boxed{\bf{\therefore \angle C + \angle B = \angle A}}}$

Now , substituting the values of ∠B (in terms of x) , ∠C (in terms of x) and ∠A , we get :-

$:\implies \bf{\angle C + \angle B = \angle A} \\ \\ \\ :\implies \bf{2x + 3x = 120^{\circ}} \\ \\ \\ :\implies \bf{5x = 120^{\circ}} \\ \\ \\ :\implies :\implies \bf{x = 120^{\circ}} \\ \\ \\ :\implies :\implies \bf{5x = \dfrac{120^{\circ}}{5}} \\ \\ \\ :\implies :\implies \bf{x = 24^{\circ}} \\ \\ \\ \therefore \bf{x = 24^{\circ}}$

Hence, the value of x is 24°.

Now substituting the value of x in the value of ∠B and ∠C (In terms of x) , we get :-

⠀⠀⠀⠀⠀⠀⠀To Find the value of ∠C :

$:\implies \bf{\angle C = 2x}$

$:\implies \bf{\angle C = 2 \times 24^{\circ}}$

$:\implies \bf{\angle C = 48^{\circ}}$

Hence, ∠C is 48°.

⠀⠀⠀⠀⠀⠀⠀To Find the value of ∠B :

$:\implies \bf{\angle B = 3x}$

$:\implies \bf{\angle B = 3 \times 24^{\circ}}$

$:\implies \bf{\angle B = 72^{\circ}}$

Hence, ∠B is 72°.

Thus , the value of ∠B is 72° and ∠C is 48°.