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Question
Find the values of x and y using the information shown in the figure.
Find the measure of ∠ABD and m∠ACD.
Solution
In ΔABC, AB = AC
∴ ∠ABC ≅ ∠ACB ...(Isosceles triangle theorem)
∴ ∠ACB = 50° ...(given)
∴ ∠ABC = 50° i.e. x = 50°
In ΔBDC, DB = DC
∴ ∠DBC = ∠DCB ...(Isosceles triangle theorem)
∠DBC = 60° ...(given)
∠DCB = 60° i.e. y = 60°
Now, ∠ABD = ∠ABC + ∠DBC ...(Angle addition property)
= 50° + 60°
= ∠ABD = 110°
Also, ∠ACD = ∠ACB + ∠DCB ...(Angle addition property)
= 50° + 60°
= 110°
∠ACD = 110°
Hence, the values of x = 50° and y = 60°, ∠ABD = 110° and ∠ACD = 110° respectively.
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