Triangle ABC-isosceles (AB = BC). BD median. Angle ABD = 40. What are the angles of triangle BDC.

It is known:

Triangle ABC – isosceles;

AB = BC;

BD is the median.

Angle ABD = 40 °.

Find what the angles of the triangle BDC are equal to.

1) Since the median divides the AC side of the ABC triangle in half, then the median BD in the isosceles triangle is the height of the ABC triangle.

This means that the angle BDA = 90 °.

2) Consider a triangle ABD.

Angle BAD = 180 ° – Angle ABD – Angle BDA = 180 ° – 40 ° – 90 ° = 90 ° – 40 ° = 50 °.

2) Since triangle ABC is isosceles, then angle A = angle C = 50 °.

3) Consider the BDC triangle.

Angle C = 50 °;

Angle D = 90 °;

Angle B = 180 ° – 90 ° – 50 ° = 40 °.