Q1: Can a triangle exist with side lengths 4 cm, 5 cm, and 10 cm?
Ans: No.
Explanation: Apply the triangle inequality: 4 + 5 = 9 < 10, so the condition fails. A triangle cannot exist.
Q2: What is the third angle in a triangle with angles 35 degrees and 65 degrees?
Ans: 80 degrees.
Explanation: The angle sum property gives:
35° + 65° + Angle 3 = 180°.
Thus, Angle 3 = 180° – 100° = 80°
Q3: Is a triangle with side lengths 7 cm, 7 cm, and 7 cm equilateral?
Ans: Yes.
Explanation: All sides are equal (7 cm), so by definition, the triangle is equilateral.
Q4: Find the exterior angle at vertex B in triangle ABC if angle A = 40 degrees and angle C = 60 degrees.
Ans: 100°.
Explanation: First, angle B = 180° – (40° + 60°) = 80°.
The exterior angle at B is 180° – 80° = 100°.
Q5: If two sides of a triangle are 6 cm and 8 cm, what is the minimum integer length of the third side?
Ans: 3 cm
Explanation: The triangle inequality requires 6 + x > 8, so x > 2.
The smallest integer is 3 cm.
Q6: In triangle DEF, if angle D = 90 degrees and angle E = 45 degrees, what is angle F?
Ans: 45°.
Explanation: Angle sum: 90°+ 45° + Angle F = 180°.
Thus, Angle F = 180° – 135° = 45°.
Q7: Can a triangle have angles 50 degrees, 60 degrees, and 80 degrees?
Ans: No
Explanation: Sum of angles:
50 + 60 + 80 = 190 > 180, so a triangle cannot exist with these angles.
Q8: What is the largest possible integer length of the third side in a triangle with sides 5 cm and 9 cm?
Ans: 13 cm.
Explanation: Triangle inequality: 5 + 9 > x, so x < 14.
The largest integer is 13 cm.
Q9 Classify a triangle with angles 30 degrees, 60 degrees, and 90 degrees by angle type.
Ans: Right-angled.
Explanation: One angle is 90 degrees, so the triangle is right-angled.
Q10: In triangle XYZ, if angle X = angle Y and angle Z = 50 degrees, what is angle X?
Ans: 65°.
Explanation: Since angle X = angle Y, let each be x.
Angle sum: x + x + 50° = 180°.
Thus, 2x = 130°
⇒ x = 65°.