The sum of the measures of the angles of a triangle is 180°
Find the three angles of a triangle if one angle is 20° greater than the smallest angle and the third angle is twice the smallest angle.
three angles is a, b, c
a+b+c=180
one angle is 20 => a=20
greater than the smallest angle and the third angle is twice the smallest angle. => a is the smallest angles
the third angle is twice the smallest angle => c=2a = 40
=> b= 120
To find the three angles of the triangle, we can start by assigning a variable to represent the smallest angle. Let's call it "x".
According to the problem, one angle is 20° greater than the smallest angle, which means the second angle can be represented as "x + 20°".
The third angle is twice the smallest angle, so it can be represented as "2x".
We know that the sum of the measures of the angles of a triangle is 180°. Therefore, we can set up the equation:
x + (x + 20°) + 2x = 180°
Now, we can solve for x:
4x + 20° = 180°
Subtracting 20° from both sides:
4x = 160°
Dividing by 4:
x = 40°
So, the smallest angle is 40°.
Now we can find the other angles using the information we have:
Second angle: x + 20° = 40° + 20° = 60°
Third angle: 2x = 2*40° = 80°
Therefore, the three angles of the triangle are 40°, 60°, and 80°.