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 * ∠C
And 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