triangle ABC is isoceles with segment AB congruent tp segment AC. Angle A is 50. The bisectors of angle B and angle C meet at D. Find the measure of angle BDC
since BAC = 50, ABC and ACB = 65
so, DBC = DCB = 32.5 and BDC = 180-65 = 115
To find the measure of angle BDC, we can start by understanding the properties of an isosceles triangle.
Given that triangle ABC is isosceles, we know that angle B is congruent to angle C. Since angle A is also given, we can find the measures of angles B and C.
Since angle A is 50 degrees and the sum of angles in a triangle is always 180 degrees, we can find the measure of angles B and C as follows:
Sum of angles B and C = 180 - angle A
Sum of angles B and C = 180 - 50
Sum of angles B and C = 130
Since triangle ABC is isosceles, segment AB is congruent to segment AC. This implies that angles B and C are congruent. Therefore:
angle B = angle C = (Sum of angles B and C) / 2
angle B = angle C = 130 / 2
angle B = angle C = 65
Now, let's move on to finding the measure of angle BDC.
The bisectors of angles B and C meet at point D. The bisector of an angle cuts the angle into two congruent angles. Therefore, angle BDC is congruent to half of angles B and C.
angle BDC = (angle B + angle C) / 2
angle BDC = (65 + 65) / 2
angle BDC = 130 / 2
angle BDC = 65 degrees
Therefore, the measure of angle BDC is 65 degrees.