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