Question

A triangle has one angle, A, that measures 20° more than twice the smallest angle, C. The largest angle, B, is 10 less than the sum of the other two angles. The sum of the angles of a triangle is 180°.

a) A = 2C + 20, B = A + C - 10, A + B + C = 180
b) A = 2C - 20, B = A + C + 10, A + B + C = 180
c) A = 20 - 2C, B = A - 10 + C, A + B + C = 180
d) A = 2C + 20, B = A - C - 10, A + B + C = 180

Answer 1

Option (a) is correct because it states angle A is 20° more than twice the smallest angle C and angle B is 10° less than the sum of the other two angles, totaling 180° for all angles in a triangle.

Step-by-step explanation:

A student is working with a problem involving the angles in a triangle. The student needs to figure out the correct relationships between the angles based on the clues given. The correct relationships between the angles of the triangle are that angle A is 20° more than twice the smallest angle C, and the largest angle B is 10° less than the sum of the other two angles with the total sum being 180°.

By using these clues, we should identify the correct set of equations from the multiple options presented, which accurately depict the relationships between the angles. Based on the sum of the angles in a triangle (180°) and given statements:

• Angle A: A = 2C + 20
• Angle B: B = A + C - 10
• The sum of angles: A + B + C = 180

Option (a) is the correct one among the choices provided as it satisfies the given conditions for the angles of the triangle.