The angle bisector of one angle of a triangle forms two angles that measure 27 degrees. The angle bisector of another angle forms two angles that measure 34 degree. What is the measure of the third angle of the triangle?
A line that bisects an angle divides it into two congruent parts.
A triangle = 180 degrees
2(27) + 2(34) + x = 180
x = ?
To find the measure of the third angle in the triangle, we can use the fact that the sum of the interior angles of any triangle is always 180 degrees.
Let's assume that the angle bisector of the first angle divides it into two smaller angles, one of which measures 27 degrees. Therefore, the other smaller angle formed by the angle bisector of the first angle would also measure 27 degrees, making the original angle 2 * 27 = 54 degrees.
Similarly, the angle bisector of the second angle divides it into two smaller angles, one of which measures 34 degrees. Therefore, the other smaller angle formed by the angle bisector of the second angle would also measure 34 degrees, making the second original angle 2 * 34 = 68 degrees.
Now, let's find the measure of the third angle by subtracting the sum of the two known angles from 180 degrees:
Third angle = 180 - (54 + 68) = 180 - 122 = 58 degrees
Thus, the measure of the third angle of the triangle is 58 degrees.