Very Short Question Answers: A Tale of Three Intersecting Lines

Q1: Can a triangle exist with side lengths 4 cm, 5 cm, and 10 cm? 

Ans: No.
Explanation: By the triangle inequality, the sum of any two sides must be greater than the third side. Here 4 + 5 = 9, and 9 < 10, so this condition fails. Therefore, a triangle with these side lengths cannot exist.

Q2: What is the third angle in a triangle with angles 35 degrees and 65 degrees? 

Ans: 80 degrees.
Explanation: Using the angle-sum property of a triangle:
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 three sides are equal (7 cm each). By definition, a triangle with all sides equal is an equilateral triangle. Its internal angles are also equal (each 60°).

Q4: Find the exterior angle at vertex B in triangle ABC if angle A = 40 degrees and angle C = 60 degrees. 

Ans: 100°.
Explanation:  The exterior angle at B is equal to the sum of the two remote interior angles, A and C. So exterior angle at B = 40° + 60° = 100°. (Alternatively, interior angle B = 180° - (40° + 60°) = 80°, and exterior = 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 inequalities give:
6 + x > 8 ⇒ x > 2, and also |6 - 8| < x ⇒ x > 2.
So the third side must be greater than 2 cm. The smallest integer greater than 2 is 3 cm.

Q6: In triangle DEF, if angle D = 90 degrees and angle E = 45 degrees, what is angle F? 

Ans: 45°.
Explanation: Using the angle-sum property:
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: The sum of the given angles is 50° + 60° + 80° = 190°, which is greater than 180°. Since the interior angles of a triangle must add up to exactly 180°, such a triangle cannot exist.

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: By the triangle inequality, the third side x must satisfy x < 5 + 9 = 14. Hence the largest integer less than 14 is 13 cm. (Also note x > |9 - 5| = 4, so x must be between 4 and 14.)

Q9 Classify a triangle with angles 30 degrees, 60 degrees, and 90 degrees by angle type. 

Ans: Right-angled.
Explanation: One of the angles is 90°, so the triangle is a right-angled triangle. (This set of angles is a common 30°-60°-90° right triangle.)

Q10: In triangle XYZ, if angle X = angle Y and angle Z = 50 degrees, what is angle X? 

Ans: 65°.
Explanation: Let each of angle X and angle Y be x.
x + x + 50° = 180° ⇒ 2x = 130° ⇒ x = 65°.