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In an isosceles triangle, the vertex angle measures 40┬░. What is the measure of each base angle?
50┬░
70┬░
80┬░
90┬░
70┬░
In an isosceles triangle, the two base angles are equal in measure. Given that the vertex angle is 40┬░ and the sum of all angles in a triangle is 180┬░, the sum of the two base angles is 180┬░тИТ40┬░=140┬░. Dividing this equally gives \frac{140┬░{2} = 70┬░ for each base angle.
In an isosceles triangle, the two base angles are equal in measure. Given that the vertex angle is 40┬░ and the sum of all angles in a triangle is 180┬░, the sum of the two base angles is 180┬░тИТ40┬░=140┬░. Dividing this equally gives \frac{140┬░{2} = 70┬░ for each base angle.
Think of a symmetric roof of a house where the two slanted sides meet at a peak vertex angle of 40┬░, sloping down equally to support the structure.
Sum┬аof┬аAngles=╬▒+╬▓+╬│=180┬░
Base┬аAngle=2180┬░тИТVertex┬аAngleтАЛ
The angle sum property of a triangle states that the interior angles always add up to 180┬░. In an isosceles triangle, the sides opposite the equal base angles are of equal length, leading to equal base angles by the Isosceles Triangle Theorem.
The sum of all interior angles in any triangle is always 180┬░.
An isosceles triangle has two sides of equal length and two equal base angles opposite those sides.
The vertex angle is the angle formed between the two equal sides.
Truss design in civil engineering and architecture for stability and symmetry.
Optical reflection and refraction calculations involving symmetric paths.
Option B (70┬░) is correct because \frac{180┬░- 40┬░{2} = 70┬░.
Option A (50┬░) is incorrect and results from an incorrect subtraction or division.
Option C (80┬░) is incorrect; it would correspond to a vertex angle of 20┬░.
Option D (90┬░) is incorrect as a base angle cannot be 90┬░ when the vertex angle is 40┬░ without violating the 180┬░ sum rule.
B is correct тАФ each base angle measures 70┬░ because the remaining 140┬░ of the triangle's angle sum is split equally between the two identical base angles.
Always verify that the sum of the three angles equals 180┬░ when solving triangle geometry problems to avoid arithmetic errors.
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