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jmc

geometry junior

Problem

If

∠ CBD

is a right angle, then this protractor indicates that the measure of

∠ ABC

is approximately

problem

(A)

2 0^{\circ}

(B)

4 0^{\circ}

(C)

5 0^{\circ}

(D)

7 0^{\circ}

Solution

We have that

2 0^{\circ} + ∠ A B D + ∠ C B D = 16 0^{\circ}

, or

∠ A B D + ∠ C B D = 14 0^{\circ}

. Since

∠ C B D

is a right angle, we have

∠ A B D = 14 0^{\circ} - 9 0^{\circ} = 5 0^{\circ} \Rightarrow 5 0^{\circ}

.

Final answer

C