A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)
Let x = smallest angle, then 11x = largest and 11x - 27º is the third.
x + 11x + (11x-27º) = 180º
Solve for x, then the other angles.
x^2-25/x^2+11x+24
Let the smallest angle be x
Then the largest angle is 11x
Therefore the third angle is 11x-27 as the
Third angle is 27 less than the largest angle.
By angle sum property of a triangle we get
X +11x+11x-27 =180 degrees
By simplification,
23x-27=180 degrees
23x=180+27=207
X=207/23
X=9 degrees
We clearly get the angles as 9,99,72
Hope this satisfies your qurstion
Where did you find answers 99, and 72 for this problem?
To solve this problem, we can let the smallest angle be represented by x°.
We are given that the largest angle is 11 times the smallest angle, so the largest angle is 11x°.
The third angle is 27° less than the largest angle, so the third angle is (11x° - 27°).
Since the sum of the angles in a triangle is 180°, we can set up an equation:
x° + 11x° + (11x° - 27°) = 180°
Combining like terms, we get:
23x° - 27° = 180°
To isolate x, we can add 27° to both sides:
23x° = 207°
Next, divide both sides by 23:
x° = 9°
Therefore, the smallest angle is 9°.
The largest angle is 11 times the smallest angle, which is 11 * 9° = 99°.
The third angle is 27° less than the largest angle, which is 99° - 27° = 72°.
So, the measure of each angle is 9°, 72°, and 99°.