Question
Download Solution PDFIn a triangle ABC, AB = AC. BC is extended to D such that CD = AB and the angle ADC is 30°. What are the angles of triangle ABC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In triangle ABC, AB = AC.
BC is extended to D such that CD = AB and ∠ADC = 30°.
Formula used:
In an isosceles triangle, the base angles are equal.
The sum of angles in any triangle = 180°.
Calculation:
Since AB = AC and CD = AB
So, AB = AC = CD
In Δ ACD,
AC = CD
So, ∠ ADC = ∠ DAC = 30°
And, ∠ ACD = 180 - (∠ ADC + ∠ DAC)
⇒ ∠ ACD = 180 - (30 + 30) = 180 - 60 = 120°
Now,
∠ ACB = 180 - ∠ ACD = 180 - 120 = 60°
Since AB = BC,
∠ ABC = ∠ ACB = 60°
Since two angles of a triangle are 60°, so third angle also will be 60° (as sum of angles of a triangle is 180°)
Hence, the angles of triangle ABC are 60°, 60°, and 60°.
Last updated on May 28, 2025
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