Classify the triangle from angle relations: In ΔABC, ∠A = x°, ∠B = y°, ∠C = (y + 20)°, and 4x − y = 10. Classify the triangle (right, obtuse, etc.).

Introduction / Context:
We are given linear relations among the angles of a triangle and must identify the triangle type. The sum of internal angles equals 180°, which together with the linear condition determines all angles.

Given Data / Assumptions:

• ∠A = x°, ∠B = y°, ∠C = (y + 20)°.
• 4x − y = 10.
• x + y + (y + 20) = 180.

Concept / Approach:
Combine the angle-sum equation with 4x − y = 10 to solve for x and y, then compute ∠C and identify if any angle equals 90°.

Step-by-Step Solution:
Angle sum: x + 2y + 20 = 180 ⇒ x + 2y = 160.From 4x − y = 10 ⇒ y = 4x − 10.Substitute into x + 2(4x − 10) = 160 ⇒ x + 8x − 20 = 160 ⇒ 9x = 180 ⇒ x = 20.Then y = 4(20) − 10 = 70.∠C = y + 20 = 70 + 20 = 90°.

Verification / Alternative check:
Angles become 20°, 70°, 90°, which sum to 180° and include a right angle at C.

Why Other Options Are Wrong:
Obtuse or equilateral cannot occur with a 90° angle and non-equal angles.

Common Pitfalls:
Arithmetic slips solving the linear system, or misassigning which angle is 90°.

Final Answer:
Right-angle