Question

What is the value for y? Enter your answer in the box. y = An isosceles triangle A B C with horizontal base B C and vertex A is above the base. Side A C and C B are labeled with single tick mark. All the three angles are labeled. Base angles C A B is labeled as 50 degrees and angle C B A is labeled as 2x degrees. The angle A C B is labeled left parenthesis 5 y plus 10 right parenthesis degrees.

Answer 1

Answer:

x = 25

y = 14

Explanation:

The described scenario can be represented using the attached triangle.

1- getting the value of x:

We know that ΔABC is an isosceles triangle with AC = BC

This means that:

∠CAB = ∠CBA

We know that ∠CAB = 50° and ∠CBA = 2x°

Equating the two angles, we get:

50 = 2x .................> Divide both sides by 2

x = 25

2- getting the value of y:

We know that the sum of the internal angles of a triangle is 180°

This means that:

∠ABC + ∠CAB + ∠ACB = 180°

We have:

∠ABC = 2x = 50°

∠ACB = 5y + 10

∠CAB = 50°

Now, we substitute to get the value of y as follows:

50 + 50 + 5y + 10 = 180

110 + 5y = 180

5y = 180 - 110

5y = 70 .............> Divide both sides by 5

y = 14

Hope this helps :)