Question

50. In the figure above, ABC is a triangle in which AD

= BD = CD.
the angle ABC is
(A) 40°
(B) 50°
(C) 80°
(D) 90°​

Answer 1

complete question:

AD = BD = CD. If angle BAD = 50°, what is angle ABC?

(Note: figure not drawn to scale.)

Answer:

(D) 90°​

Explanation:

The figure below is the triangle for the complete question. The side AD = BD = CD. The triangle ABD is an isosceles triangle . AD and BD are equal. Since the angle BAD = 50° , angle ABD = 50°.

Sum of angle in a triangle = 180°

triangle ADB = 180 - 50 + 50 = 80°

Angle BDC = 180 - 80 = 100°. (angle on a straight line)

Since BD and CD are equal(Isosceles triangle) the angle DBC and DCB are equal. The angle DBC and DCB = 80/2 = 40°.

angle ABC = angle ABD + angle DBC

angle ABC = 50° + 40°

angle ABC = 90°