Concept:The sum of angles in a triangle is 180 degrees, and the properties of different types of triangles based on their angles.Explanation:We are given a triangle ABC where angle A is 60 degrees and angle B is 4 times angle C. We know that the sum of all angles in a triangle is always 180 degrees.Let's use this information to find the values of angles B and C.We have:∠A = 60°∠B = 4 * ∠CAnd the sum of angles in a triangle is:∠A + ∠B + ∠C = 180°Substitute the given values into the equation:60° + (4 * ∠C) + ∠C = 180°Combine the terms with ∠C:60° + 5 * ∠C = 180°Now, isolate 5 * ∠C by subtracting 60° from both sides:5 * ∠C = 180° - 60°5 * ∠C = 120°Find the value of ∠C by dividing by 5:∠C = 120° / 5∠C = 24°Now, we can find ∠B using the relation ∠B = 4 * ∠C:∠B = 4 * 24°∠B = 96°So, the angles of the triangle are:∠A = 60°∠B = 96°∠C = 24°An obtuse-angled triangle is a triangle where one of the angles is greater than 90 degrees. Since ∠B is 96°, which is greater than 90°, triangle ABC is an obtuse-angled triangle.Answer:Obtuse angled