The measure of angle ABC and BDC is 80° and 90° respectively.
In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.
We have to find the measure of angle ∠ABC and ∠BDC.
As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.
[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]
Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.
∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
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