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In an isosceles triangle, if the vertex angle is 40 degrees, what is the measure of each base angle?
60 degrees
70 degrees
80 degrees
50 degrees
70 degrees
In an isosceles triangle, the angles opposite to the equal sides are equal. Since the sum of all interior angles of any triangle is 180┬░, we can find the base angles by subtracting the vertex angle from 180┬░ and dividing the remainder by 2.
In an isosceles triangle, the angles opposite to the equal sides are equal. Since the sum of all interior angles of any triangle is 180┬░, we can find the base angles by subtracting the vertex angle from 180┬░ and dividing the remainder by 2.
Think of a balanced seesaw where the two sides (base angles) must share the weight equally after the top (vertex angle) is fixed.
Sum is 180, vertex is separate, divide the rest by two to keep it balanced.
V+2B=180┬░ тАФ Relationship between vertex angle V and base angles B in an isosceles triangle
B=2180┬░тИТVтАЛ тАФ Formula to calculate the measure of a base angle
The Angle Sum Property states that the sum of interior angles in a triangle is constant at 180┬░. For an isosceles triangle with vertex angle V and base angles B, the relationship is given by V+2B=180┬░. Substituting V=40┬░, we get 40┬░+2B=180┬░, leading to 2B=140┬░ and B=70┬░.
The sum of interior angles in any Euclidean triangle is always 180┬░.
In an isosceles triangle, the two base angles are congruent (equal).
The vertex angle is the angle formed by the two equal sides.
Simplifies calculation of unknown angles in geometric proofs.
Applicable only to Euclidean geometry; non-Euclidean triangles have angle sums юАа=180┬░.
Structural engineering for roof trusses.
Navigation and triangulation calculations.
The vertex angle 40┬░ is an acute angle, resulting in base angles that are also acute.
Option A (60┬░) describes an equilateral triangle (60┬░,60┬░,60┬░). Option D (50┬░) would result in a sum of 40+50+50=140┬░, failing the triangle angle sum rule.
B is correct тАФ Using the angle sum property of triangles, 180┬░тИТ40┬░=140┬░, and dividing by two gives 70┬░.
Always verify if your calculated angles sum to 180┬░ as a quick check for any triangle geometry problem.