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30 Sep 2024, 09:03
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:08) correct
0% (00:00) wrong based on 1 sessions
History
Date
Time
Result
Not Attempted Yet
AB = BC
Quantity A
x
Quantity B
120
Attachment:
1234.jpg [ 10.39 KiB | Viewed 697 times ]
02 Mar 2025, 11:55
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OE
Note that there are four angles in the fgure: the three interior angles of triangle ABC and the exterior angle at vertex A. Since the measure of the exterior angle at vertex A is x degrees, it follows that the measure of interior angle A is (180 - x)°. Also, since AB = BC, it follows that triangle ABC is isosceles and the measures of interior angles A and C are equal. Terefore the measure of interior angle C is also (180 - x)°. Since the sum of the measures of the interior angles of a triangle is 180° and you are given that the measure of interior angle B is 40°, it follows that \(40 + (180 - x) + (180 - x) = 180.\) Solving the equation for x gives x = 110. Since Quantity B is 120, the correct answer is Choice B.
Answer: B
Note that there are four angles in the fgure: the three interior angles of triangle ABC and the exterior angle at vertex A. Since the measure of the exterior angle at vertex A is x degrees, it follows that the measure of interior angle A is (180 - x)°. Also, since AB = BC, it follows that triangle ABC is isosceles and the measures of interior angles A and C are equal. Terefore the measure of interior angle C is also (180 - x)°. Since the sum of the measures of the interior angles of a triangle is 180° and you are given that the measure of interior angle B is 40°, it follows that \(40 + (180 - x) + (180 - x) = 180.\) Solving the equation for x gives x = 110. Since Quantity B is 120, the correct answer is Choice B.
Answer: B
