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In an isosceles triangle, the vertex angle measures 132°. What is the measure of each of the base angles?
11° and 8°
24° and 24°
27° and 21°
4° and 10°
24° and 24°
In an isosceles triangle, the two base angles are congruent. Since the sum of all interior angles in any triangle is 180°, subtracting the vertex angle from 180° leaves the sum of the two base angles.
In an isosceles triangle, the two base angles are congruent. Since the sum of all interior angles in any triangle is 180°, subtracting the vertex angle from 180° leaves the sum of the two base angles.
Think of a symmetric roof frame; if the peak is pushed up high (wide angle), the two sides must tilt at the same shallow angle to keep the structure balanced.
V + 2B = 180: Vertex plus two Bases equals 180.
∠V+2∠B=180° — Relationship between vertex and base angles in an isosceles triangle
∠B=2180°−∠V — Formula to calculate base angle
The Angle Sum Property states that the sum of the interior angles of a triangle is always 180°. For an isosceles triangle with base angles α, the equation is v+2α=180°, where v is the vertex angle. Substituting v=132° yields 2α=180°−132°=48°, resulting in α=24°.
Isosceles triangles have exactly two equal sides and two equal base angles.
The sum of interior angles in a Euclidean triangle is always a constant 180°.
If the vertex angle is obtuse (>90°), the base angles must be acute (<45°).
Simplifies geometric calculations by using symmetry
Structural engineering for roof trusses
Design of stable mechanical supports
The sum of angles 132°+24°+24°=180°.
Option A, C, and D do not satisfy the property that the base angles in an isosceles triangle must be equal.
B is correct — Using the angle sum property, subtracting 132° from 180° leaves 48°, which split equally between the two base angles results in 24° each.
Whenever you see 'isosceles', immediately remember two sides are equal and two angles are equal; this is the key to solving 90% of triangle geometry problems.
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