2007 AMC 10A Problem 8

Attempt Problem 8 of the 2007 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 10A solutions, or check the answer key.

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8.

Triangles

ABC

and

ADC

are isosceles with

AB = BC

and

AD = DC.

Point

D

is inside

\triangle ABC,

\angle ABC = 40^\circ,

and

\angle ADC = 140^\circ.

What is the degree measure of

\angle BAD?

20

30

40

50

60

Answer: D

Concepts:isosceles triangle angle chasing

Difficulty rating: 1170

Small hint:

In an isosceles triangle the two base angles are equal

Big hint:

Find

\angle BAC

and

\angle DAC,

then subtract

Solution:

Since

\triangle ABC

is isosceles,

\angle BAC = \tfrac12(180^\circ - 40^\circ) = 70^\circ.

Since

\triangle ADC

is isosceles,

\angle DAC = \tfrac12(180^\circ - 140^\circ) = 20^\circ.

Therefore

\angle BAD = \angle BAC - \angle DAC

= 70^\circ - 20^\circ

= 50^\circ.

Thus, the correct answer is D.