find the angle ABD
angle A=70°
Angle C= 50°
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To construct a quad ABCD,
In triangle ABC where angle B =70 degree and angle C =50 degree, and
Given AB = BD and AC =DC (similar as AB/AC=BD/DC)
Therefore, Quad ABCD consists of 2 congruent scalene triangles opposite each other.
To find angle BAD, Join AD in quad ABCD. Therefore, 2 different isosceles triangles are constructed - triangle BAD and triangle CAD. In triangle ABC, angle B = 70 degree (given), angle ABD = 70 x 2 = 140 degree (property of isosceles triangle).
Therefore, angle BAD = (180 - 140) ÷ 2 degree = 20 degree.
Metacognitive analysis:
To prove that angle BAD= 20 degree
Similarly, angle CAD = 40 degree.
Sum of angles in a QUAD = 360 degree :
Angle A = 60 + Angle B 140 + Angle C 100 + Angle D =60
Therefore, angle BAD is 20 degree.
Answer: 20 degree
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