Question

In isosceles triangle ABC, if ma) 35°
b) 45°
c) 55°
d) 65°

Answer 1

In an isosceles triangle ABC, if angle A = angle B, then the possible measures for angle A or angle B are options b) 45° and c) 55°.

Explanation:

In an isosceles triangle, angles opposite the congruent sides are also congruent. Given that angles A and B in triangle ABC are equal, let's consider their possible measures.

If angle A is 45°, then angle B will also be 45° since they are equal in an isosceles triangle. This satisfies the condition of angle A being equal to angle B in the triangle.

Similarly, if angle A is 55°, angle B will also be 55°, maintaining the equality of angles in the isosceles triangle. These two options, 45° and 55°, align with the property of an isosceles triangle where the base angles (angles A and B) are equal.

However, options 35° and 65° are not possible as they do not meet the condition of having equal measures for angles A and B in an isosceles triangle.

Therefore, considering the property of an isosceles triangle where angles opposite equal sides are congruent, the valid measures for angle A or angle B in this case are 45° and 55°, as provided in options b) and c).

Answer 2

In an isosceles triangle, the two base angles are congruent. In this case, if angle A is 35°, then angle B is 110° and angle C is 35°.

Step-by-step explanation:

In an isosceles triangle, the two base angles are congruent.

Let's assume that angle A is 35°. Since the triangle is isosceles, angle C must also be 35°. Now, we can use the fact that the sum of the angles in a triangle is 180°. So, 35° + 35° + angle B = 180°. Solving for angle B, we get angle B = 180° - 35° - 35° = 110°.

Therefore, the measures of the angles in isosceles triangle ABC are angle A = 35°, angle B = 110°, and angle C = 35°.