2000 AMC 8 Problem 24

Attempt Problem 24 of the 2000 AMC 8 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 2000 AMC 8 solutions, or check the answer key.

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24.

If

\angle A = 20^\circ

and

\angle AFG =\angle AGF,

then

\angle B+\angle D =

48^\circ

60^\circ

72^\circ

80^\circ

90^\circ

Answer: D

Concepts:angle chasing isosceles triangle

Difficulty rating: 1580

Small hint:

Use the isosceles triangle

AFG

first

Big hint:

Then use the angle sum of

\triangle BFD

Solution:

In

\triangle AFG,

the two base angles are equal and

\angle A=20^\circ,

so

\begin{aligned} \angle AFG &= \angle AGF \\ &= \frac{180^\circ-20^\circ}{2} \\ &= 80^\circ. \end{aligned}

Since

\angle AFG

and

\angle BFD

form a straight angle,

\angle BFD=100^\circ.

In

\triangle BFD,

\angle B+\angle D=180^\circ-100^\circ=80^\circ.

Thus, D is the correct answer.