Angle A = 19.7 Angle B = ? Angle C = ?

Question

In triangle abc the size of angle b is 5 times the size of angle a and the size of angle c is 17 degrees lessthan 4 times the size of angle a.

Answer 1

Angle B:

We are given that the size of Angle B is equal to 5 times the size of angle A.

In word problems, the word "times" indicates multiplication.

As such, we can set up an equation for finding angle B:

Angle B = 5 * (Angle A)

Since we know that Angle A = 19.7 degrees, we can solve for Angle B:

Angle B = 5 * 19.7 degrees

Angle B = 98.5 degrees

Angle C:

We are given that Angle C is 17 degrees less than 4 times the size of angle A.

In word problems, words such as "less" or "fewer" indicate subtraction.

Additionally, as mentioned before, "times" indicates multiplication.

Therefore, we can write an equation for Angle C in terms of Angle A.

Angle C = 4 * (Angle A) - 17

Since we know that Angle A = 19.7 degrees, we can solve for Angle C:

Angle C = (4 * 19.7 - 17) degrees

Angle C = 61.8 degrees

Checking Work:

Knowing that the angles of a triangle sum up to 180 degrees, we can check to see if Angle A, Angle B, and Angle C sum up to 180 degrees.

Angle A + Angle B + Angle C = 19.7 degrees + 61.8 degrees + 98.5 degrees = 180 degrees

Hope this explanation helped :)

Answer 2

Angle B = 5(19.7)

Angle C = 4(19.7) - 17