In the quadrilateral ABCD, in which angle A = 60° and angle B = 50°. The measure of angles C and D are,
∠C = 200° and ∠D = 50°
In the quadrilateral ABCD, it is given that,
A = 60° and angle B = 50°
Now, since AC is the angle bisector of angles A and C, we have,
∠DAC = ∠BAC ......... (1)
And ∠ACD = ∠ACB ............ (2)
Also, AC divides the quadrilateral ABCD into two triangles, ΔABC and ΔACD.
In ΔABC, ∠BAC = 30° [from (2)] and ∠ABC = 50°
Using angle sum property of a triangle, we have,
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 30° + 50° + ∠ACB = 180°
80° + ∠ACB = 180°
∠ACB = 180° - 80°
∠ACB = 100°
From (1), ∠ACD = ∠ACB = 100°
∠C = ∠ACD + ∠ACB
⇒ ∠C = 100° + 100°
∠C = 200°
Now, according to the angle sum property of a quadrilateral,
∠A + ∠B + ∠C + ∠D = 360°
Substituting the values of ∠A, ∠B, and ∠C, we get,
60° + 50° + 200° + ∠D = 360°
310° + ∠D = 360°
∠D = 360° - 310°
∠D = 50°
Hence, in quadrilateral ABCD, ∠C = 200° and ∠D = 50°
Learn more about a quadrilateral here:
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