in triangle ABC, angle b is 5 more than twice angle A and angle C iss 35 less than three times angle A. Find the angles of triangle ABC
You'd have to set up equations.
First, let a=angle A, b=angle B and c=angle C, all in degrees.
(Note: in solving math problems, it is important to define all symbols/variables used, including the units).
We are given:
"angle b is 5 more than twice angle A" which translates to:
b=2a+5 .....(1)
"angle C is 35 less than three times angle A" which means:
c=3a-35 .....(2)
Finally, we know from basic geometry that the sum of angles of a triangle is 180°, so
a+b+c=180 .....(3)
Using the three equations, we can solve for a by substitution, i.e.
Substitute values of b and c from (1) and (2) into equation (3) and solve for the value of a.
To find the angles of triangle ABC, let's assume that angle A is x degrees.
According to the information given, we can determine the measure of angle B and angle C.
Angle B is 5 more than twice angle A, so it can be expressed as:
B = 2A + 5
Angle C is 35 less than three times angle A, so it can be expressed as:
C = 3A - 35
Since the sum of the angles of a triangle is always 180 degrees, we can write the equation:
A + B + C = 180
Substituting the expressions for angles B and C, we get:
x + (2x + 5) + (3x - 35) = 180
Simplifying the equation:
6x - 30 = 180
Adding 30 to both sides:
6x = 210
x = 35
Now that we know the value of x, we can find the measures of angles A, B, and C:
A = x = 35 degrees
B = 2A + 5 = 2(35) + 5 = 75 degrees
C = 3A - 35 = 3(35) - 35 = 70 degrees
Therefore, the angles of triangle ABC are:
Angle A = 35 degrees
Angle B = 75 degrees
Angle C = 70 degrees