Answer:
Angle A = 58.57°
Angle B = 42.14°
Angle C = 80.29°
Explanation:
To find the three angles of triangle ABC, we need to set up an equation using the given angle measures.
Angle A is given as (x+35)°, angle B is given as (2x-5)°, and angle C is given as (4x-15)°.
According to the angle sum property of a triangle, the sum of all three angles in a triangle is always 180°.
So, we can set up the equation:
(x+35) + (2x-5) + (4x-15) = 180
Now, let's solve the equation to find the value of x.
Combine like terms:
7x + 15 = 180
Subtract 15 from both sides:
7x = 165
Divide both sides by 7:
x = 165/7
Simplify the fraction:
x = 23.57
Now that we have found the value of x, we can substitute it back into the expressions for angle A, B, and C to find their values.
Angle A = (23.57 + 35)° = 58.57°
Angle B = (2 * 23.57 - 5)° = 42.14°
Angle C = (4 * 23.57 - 15)° = 80.29°
Therefore, the three angles of triangle ABC are approximately:
Angle A = 58.57°
Angle B = 42.14°
Angle C = 80.29°