Since M is the intersection of the angle bisectors of angles A and B, M is the incenter of triangle ABC. This means that AM, BM, and CM are all angle bisectors of triangle ABC. Therefore, angles CAM and CBM each measure 90 degrees plus half of the measure of their corresponding angles in triangle ABC.
Since angle A measures 58 degrees, angle CAM measures 90 degrees plus half of 58 degrees, or 90 + 29 = 119 degrees.
Similarly, since angle B measures 96 degrees, angle CBM measures 90 degrees plus half of 96 degrees, or 90 + 48 = 138 degrees.
Finally, angle AMB is the sum of angles C, CAM, and CBM in triangle ABC. Since the sum of the interior angles of a triangle is always 180 degrees, we have:
angle AMB = 180 - (A + B + C) = 180 - (58 + 96 + C) = 180 - (154 + C).
Since the sum of the angle measures in triangle ABC is 180 degrees, we can substitute C = 180 - (A + B) to find:
angle AMB = 180 - (154 + (180 - (A + B)))
= 180 - (154 + (180 - (58 + 96)))
= 180 - (154 + (180 - 154))
= 180 - (154 + 26)
= 180 - 180
= <<180-180=0>>0 degrees.
Therefore, the measure of angle AMB is 0 degrees.
Angle bisectors of the angles A and B of a triangle ABC intersect each other at point M. Find the measure of AMB is the measure of angle A is 58 degrees and the measure of angle B is 96 degrees.
1 answer
1 answer