Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
In an isosceles triangle, the vertex angle measures 76°. What is the measure of each of the base angles?
32° and 49°
55° and 49°
52° and 52°
43° and 62°
52° and 52°
In an isosceles triangle, the two base angles are equal by definition. Since the sum of interior angles in any triangle is 180°, subtracting the vertex angle of 76° from 180° leaves 104° to be shared equally between the two base angles.
In an isosceles triangle, the two base angles are equal by definition. Since the sum of interior angles in any triangle is 180°, subtracting the vertex angle of 76° from 180° leaves 104° to be shared equally between the two base angles.
Think of an isosceles triangle like a roof frame; because the two sides are cut to the same length, they must meet the flat horizontal beam at identical angles to maintain symmetry.
Sum 180, Vertex subtract, Divide the rest (SVD).
Sum of angles = 180°
B=2180°−A — formula to calculate base angle B given vertex angle A
The Angle Sum Property states that the sum of angles in a triangle is always 180°. For an isosceles triangle with vertex angle A and equal base angles B, the relation is A+2B=180°. Substituting the given vertex angle, we get 76°+2B=180°, which simplifies to 2B=104°, resulting in B=52°.
An isosceles triangle has at least two equal sides and two equal opposite angles.
The sum of interior angles of any triangle in Euclidean geometry is always 180°.
Base angles are always adjacent to the third (unequal) side.
Geometric symmetry
Predictable structural properties
Architecture and truss design
Navigation and triangulation
Base angles in an isosceles triangle must always be acute (less than 90°) if the vertex angle is greater than 0°.
Options A, B, and D are incorrect as they do not sum to 180° when combined with the 76° vertex angle or fail the symmetry condition of an isosceles triangle.
C is correct — The calculation 180°−76°=104°, and 104°÷2=52°, confirms that both base angles must be 52°.
In competitive exams, always check for the 'Isosceles' condition first; if it is isosceles, you only need to perform one calculation to find both angles.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants