Question

4) In an isosceles trapezium , if one of the base angle is 65 degrees , then the other angles are ______

Answer 1

Answer:

The other angles of the isosceles triangle are 65° and 50°

Step-by-step explanation:

By definition, the base angles of an isosceles triangle are equal, therefore, we have;

Where one of the base angles = 65°, the other base angle = 65°

To find the third angle, we proceed as follows

Let the third angle = ∠3

Let the two base angles = ∠1, and ∠2 such that ∠1 = ∠2 = 65°

Where ∠1 = 65° is the known base angle

By the sum of the interior angles of a triangle theorem, we have;

∠3 + ∠1 + ∠2 = 180°

∴ ∠3 + 65 ° + 65° = 180°

∠3 = 180° - (65 ° + 65°) = 180° - 130° = 50° By angle subtraction postulate

∴  The third angle = ∠3 = 50°

The other angles of the isosceles triangle are ∠2 = 65° and ∠3 = 50°.