CBSE Class 7 Mathematics Triangles and its Properties MCQs Set 17

Answer: (b) 70°

Explanation:
1. 180° - 50° - 60° = 70°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (a) 80°

Explanation:
1. 2k + 3k + 4k = 180°, so k = 20°.
2. Largest = 4 × 20° = 80°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (d) 50°

Explanation:
1. (180° - 80°) / 2 = 50°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (c) 60°

Explanation:
1. Sum of other two = 100°. 3k + 2k = 100° gives k = 20°.
2. Larger = 60°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (b) 85°

Explanation:
1. Exterior angle = sum of interior opposite angles, so the other = 145° - 60° = 85°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (a) 60°

Explanation:
1. Exterior angle = P + Q, so P = 110° - 50° = 60°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (d) 60°

Explanation:
1. 180° / 3 = 60°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (c) 70°

Explanation:
1. (180° - 40°) / 2 = 70°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (b) 55°

Explanation:
1. 90° - 35° = 55°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (a) 120°

Explanation:
1. 180° - 60° = 120°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (d) 30°

Explanation:
1. 6x = 180°, so x = 30°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (d) 80°

Explanation:
1. Sum: (x + 20) + (2x - 10) + (3x - 10) = 6x = 180°, so x = 30°.
2. Angles: 50°, 50° and 80°. The largest is 80°.

Teacher's Note:
1. Angle sum of a triangle is 180°; an exterior angle equals the sum of the two interior opposite angles.
2. Re-check the answer by substituting back into the question.

Answer: (c) the mid point of the opposite side

Explanation:
1. By definition a median goes from a vertex to the mid point of the opposite side.

Teacher's Note:
1. An altitude, not a median, is perpendicular to the opposite side.
2. Re-check the answer by substituting back into the question.

Answer: (b) 3

Explanation:
1. One median can be drawn from each vertex, so there are 3.

Teacher's Note:
1. All three medians meet at the centroid.
2. Re-check the answer by substituting back into the question.

Answer: (a) a vertex to the opposite side (or its extension)

Explanation:
1. It is drawn from a vertex perpendicular to the line of the opposite side.

Teacher's Note:
1. In an obtuse triangle two altitudes lie outside the triangle.
2. Re-check the answer by substituting back into the question.

Answer: (d) outside the triangle

Explanation:
1. The perpendiculars from those vertices fall on the extended opposite sides, so they lie outside the triangle.

Teacher's Note:
1. In a right triangle two altitudes are the legs themselves.
2. Re-check the answer by substituting back into the question.

Answer: (c) wholly in the interior of the triangle

Explanation:
1. A median joins a vertex to a point on the opposite side, so it stays inside.

Teacher's Note:
1. This is true for every kind of triangle.
2. Re-check the answer by substituting back into the question.

Answer: (b) scalene

Explanation:
1. Unequal sides define a scalene triangle.

Teacher's Note:
1. Classify by sides first and by angles second.
2. Re-check the answer by substituting back into the question.

Answer: (a) obtuse and isosceles

Explanation:
1. One angle exceeds 90° so it is obtuse, and two angles are equal, so two sides are equal.

Teacher's Note:
1. Equal angles lie opposite equal sides.
2. Re-check the answer by substituting back into the question.

Answer: (d) greater than the third side

Explanation:
1. This is the triangle inequality.

Teacher's Note:
1. It also means the third side exceeds the difference of the other two.
2. Re-check the answer by substituting back into the question.

Answer: (c) 3 cm, 4 cm, 5 cm

Explanation:
1. 3 + 4 > 5 holds for all pairs. In the others the two smaller sides add to less than the largest.

Teacher's Note:
1. Check only the two smaller sides against the largest.
2. Re-check the answer by substituting back into the question.

Answer: (b) 12 cm

Explanation:
1. The third side must lie strictly between 5 cm and 25 cm. Only 12 cm does.

Teacher's Note:
1. The limits are the difference and the sum of the two given sides.
2. Re-check the answer by substituting back into the question.