In a triangle ABC,angle b is 4 times angle "A" and angle "C" IS 17 less than 5 times angle "A". Find the size of the angles.
let angle A = x
then angle B = 4x
and angle C = 5x-17
solve:
x + 4x + 5x - 17 = 180
Let's represent angle A as x.
According to the given information,
angle B = 4 * angle A = 4x
angle C = 5 * angle A - 17 = 5x - 17
In a triangle, the sum of all three angles is equal to 180 degrees. Therefore, we can form the following equation:
angle A + angle B + angle C = 180
Substituting the given values, we have:
x + 4x + 5x - 17 = 180
10x - 17 = 180
10x = 180 + 17
10x = 197
x = 197 / 10
x = 19.7
Now that we have the value of x, we can find the sizes of the angles:
angle A = x = 19.7 degrees
angle B = 4x = 4 * 19.7 = 78.8 degrees
angle C = 5x - 17 = 5 * 19.7 - 17 = 98.5 - 17 = 81.5 degrees
So, the size of angle A is 19.7 degrees, angle B is 78.8 degrees, and angle C is 81.5 degrees.
To solve this problem, we need to use the information given about the angles in the triangle and set up an equation.
Let's assume that angle A is x (in degrees). So, angle B will be 4x, as it is 4 times angle A. Angle C will be 5x - 17, as it is 17 less than 5 times angle A.
According to the properties of a triangle, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can write the equation:
x + 4x + 5x - 17 = 180
Simplifying the equation, we have:
10x - 17 = 180
Now, we can solve for x by isolating the variable:
10x = 180 + 17
10x = 197
x = 197/10
x = 19.7
Therefore, angle A is approximately 19.7 degrees.
To find the values of angles B and C, we can substitute the value of x back into the expressions we derived earlier:
Angle B = 4x = 4 * 19.7 = 78.8 degrees
Angle C = 5x - 17 = 5 * 19.7 - 17 = 98.5 - 17 = 81.5 degrees
So, the angles of triangle ABC are approximately:
Angle A ≈ 19.7 degrees
Angle B ≈ 78.8 degrees
Angle C ≈ 81.5 degrees