Mathematics

Mathematics

Problem

In △XYZ\triangle XYZ, two of its angles are equal. Each of these equal angles measures (3x−10)∘(3x - 10)^{\circ}, while the third angle measures (2x+20)∘(2x + 20)^{\circ}. a. (i) Write the equation obtained from the angle–sum property of a triangle. b. (ii) Solve for xx. c. (iii) Hence, determine all three angles of △XYZ\triangle XYZ.
Intuitive explanation

An isosceles triangle has two equal angles, and all three angles must sum to 180°180°. Set up an equation using this constraint: add the two equal angles and the third angle, then solve for xx. Once you find xx, you can verify your answer makes sense by checking that all three angle measures are positive and sum correctly.

Intuitive explanation

An isosceles triangle has two equal angles, and all three angles must sum to 180°180°. Set up an equation using this constraint: add the two equal angles and the third angle, then solve for xx. Once you find xx, you can verify your answer makes sense by checking that all three angle measures are positive and sum correctly.

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