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Lines, Triangles and Circles · Question 20 of 67

Question 20

MediumOriginal question

The angles of triangle ABC are ∠A=(x+15)∘\angle A = (x + 15)^\circ, ∠B=(2x−10)∘\angle B = (2x - 10)^\circ and ∠C=(3x+25)∘\angle C = (3x + 25)^\circ. What is ∠B\angle B?

Options for question 20

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Angle sum: (x+15)+(2x−10)+(3x+25)=180(x + 15) + (2x - 10) + (3x + 25) = 180.

  2. 6x+30=1806x + 30 = 180, so x=25x = 25.

  3. ∠B=2×25−10=40∘\angle B = 2 \times 25 - 10 = 40^\circ. (∠A\angle A is also 40° and ∠C\angle C is 100°.)

Worth noting

25 is xx, not the angle, and 50 is 2x2x before subtracting 10. Since ∠A=∠B\angle A = \angle B, this triangle is isosceles.

Concept
Angle sum of a triangle with algebraic angles
Typical time
70 s
Your time
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Ten questions from Lines, Triangles and Circles, at your own pace.

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