In triangle ABC, AB = AC and A = 36°. A point D on side AC is chosen so that BD = BC. What is DBC?

Lines, Triangles and Circles · Question 23 of 67

Question 23

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In triangle ABC, $AB = AC$ and $\angle A = 36^\circ$ . A point D on side AC is chosen so that $BD = BC$ . What is $\angle DBC$ ?

36°Correct answerYour answer54°Correct answerYour answer72°Correct answerYour answer108°Correct answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$AB = AC$ , so $\angle ABC = \angle ACB = (180^\circ - 36^\circ) \div 2 = 72^\circ$ .
In triangle BDC, $BD = BC$ , so $\angle BDC = \angle BCD = 72^\circ$ .
$\angle DBC = 180^\circ - 72^\circ - 72^\circ = 36^\circ$ .

Worth noting

72° is $\angle ABC$ , the whole angle at B. Only part of it lies inside triangle BDC.

Ten questions from Lines, Triangles and Circles, at your own pace.

Ten questions from Lines, Triangles and Circles, at your own pace.