Question

Given: ad^(harr)||be^(harr), (m)/(_(c))be=10\deg , (m)/(_(a))be=50\deg , bar(ac) is the angle bisector of ()/(_(d)ab) find:( m)/(_(c))

Answer 1

To find the measure of m/c, we can make use of the Angle Bisector Theorem. According to the theorem, the ratio of the lengths of the segments that the angle bisector divides the opposite side into is equal to the ratio of the lengths of the other two sides of the triangle.

Step-by-step explanation:

To find the measure of m/c, we can make use of the Angle Bisector Theorem. According to the theorem, the ratio of the lengths of the segments that the angle bisector divides the opposite side into is equal to the ratio of the lengths of the other two sides of the triangle. In this case, we are given that m/(c)be = 10° and m/(a)be = 50°. Since be is the angle bisector, we can write:

m/(c)be/m/(a)be = ac/ea.

Substituting the given values, we have:

10/50 = ac/ ea.

Cross multiplying, we get:

ac = 0.2ea.

Simplifying, we find:

m/(c) = 0.2