One of the two equal angles of an isosceles.triangle is greatest than the third angle 18° . Find the three angles of the isosceles triangle
A = greatest angle
B = smaller angle
A = B + 18°
The sum of the angles in a triangle is 180°
2 A + B = 180°
2 ( B + 18° ) + B = 180°
2 B + 2 * 18° + B = 180°
3 B + 36° = 180° Subtract 36° to both sides
3 B + 36° = 180°
3 B + 36° - 36 ° = 180° - 36°
3 B = 144° Divide both sides by 3
B = 144° / 3
B = 48°
A = B + 18°
A = 48° + 18°
A = 66°
Three angles of the triangle:
66° , 66° , 48°
Let's assume that the measure of the two equal angles is equal to x.
According to the given information, one of the equal angles is greater than the third angle by 18°. So, we can express the measure of the third angle as x - 18°.
Since the sum of the angles in a triangle is 180°, we can set up the equation:
x + x + (x - 18°) = 180°
Simplifying the equation:
3x - 18° = 180°
Adding 18° to both sides:
3x = 198°
Dividing both sides by 3:
x = 66°
Now, we can substitute the value of x back into the equation to find the measures of the angles:
First angle: x = 66°
Second angle: x = 66°
Third angle: x - 18° = 66° - 18° = 48°
So, the three angles of the isosceles triangle are 66°, 66°, and 48°.
To find the three angles of an isosceles triangle, we can use the fact that the sum of the angles of any triangle is always 180 degrees.
Let's assume that the measure of each equal angle in the isosceles triangle is x degrees.
Since one of the equal angles is greater than the third angle by 18 degrees, we can set up the following equation:
x = (third angle) + 18
Now, we can substitute the value of x in terms of the third angle into the equation for the sum of the angles:
2x + (third angle) = 180
Substituting x = (third angle) + 18, we get:
2((third angle) + 18) + (third angle) = 180
Simplifying the equation:
2(third angle) + 36 + (third angle) = 180
3(third angle) = 180 - 36
3(third angle) = 144
Dividing both sides by 3:
(third angle) = 144 / 3
(third angle) = 48
Now that we have the measure of the third angle, we can find the other two angles:
x = (third angle) + 18
x = 48 + 18
x = 66
Therefore, the three angles of the isosceles triangle are 66°, 66°, and 48°.