The Question is:
Three angles in a triangle are given by 4x+10, 3x+15, and 2x+20.
a) Draw a diagram, and write an equation linking these angles together.
b) Solve the equation for x.
c) State the value of the three angles in the triangle.
What I want to know:
- What type of triangle would it be?
- How would you write an equation that shows their 'relationship' with one another?
- Where would you start when solving for x?
4x+10 + 3x+15 + 2x+20 = 180
find x, and then the rest is easy
4x+10+3x+15+ 2x+20=180
9x+45=180
Divide through by 9
x+5=20
X=20-5=15
Plug the value of x into
(4x+10)°=
(3x+15)°=
(2x+20)°=
To determine the type of triangle and write an equation linking the angles together, you can use the fact that the sum of angles in a triangle is always 180 degrees.
a) To draw a diagram, label the angles as A, B, and C, and let the measurements be 4x+10, 3x+15, and 2x+20.
The equation linking these angles together is: (4x+10) + (3x+15) + (2x+20) = 180
b) To solve the equation for x, combine like terms:
4x + 10 + 3x + 15 + 2x + 20 = 180
9x + 45 = 180
Subtract 45 from both sides:
9x = 135
Divide both sides by 9:
x = 15
c) To find the values of the three angles in the triangle, substitute x = 15 into 4x+10, 3x+15, and 2x+20:
Angle A = 4x + 10 = 4(15) + 10 = 60 + 10 = 70 degrees
Angle B = 3x + 15 = 3(15) + 15 = 45 + 15 = 60 degrees
Angle C = 2x + 20 = 2(15) + 20 = 30 + 20 = 50 degrees
Therefore, the three angles in the triangle are 70 degrees, 60 degrees, and 50 degrees.
Regarding the type of triangle, we can determine it based on the angles:
- Since all angles are less than 90 degrees, it would be an acute triangle.