Question

An isosceles triangle with vertices labeled A, B, and C. Side B C is the base. Sides A B and A C are equal. Sides A B and A C are labeled with single tick marks. Angle A is labeled as (4 y plus 10 )degrees, angle B is labeled as 75 degrees, and angle C is labeled as (3 x )degrees.

Answer 1

Angle A = 30degree, Angle B = 75degree, Angle C = 75degree, x=25, y=5

Explanation:

We are given isosceles triangle with vertices named as A, B and C. Firstly, the variables x and y are calculated then we'll find all the three angles.

Finding x

As the base angles of the same sides are equal.

∠B = ∠C

⇒

75 = 3x

75/3 = x

25 = x

Finding y

The some of all the internal angles of a triangle is 180 degree.

So,

∠A + ∠B + ∠C = 180

(4y+10) + (75) + (3x) = 180

4y+10+75+3(25) = 180

4y + 160 = 180

4y = 180-160

y = 5

Finding angles

∠A = 4y+10

∠A = 4(5)+10

∠A = 30

∠B = 75

∠C = 3x

∠C = 3(25)

∠C = 75

(or alternatively as ∠B = ∠C, so it can directly be stated that ∠C = 75 degree)