Question:
In the figure (not drawn to scale) given below, if $AD = CD = BC$ and $\angle DBC = 96^\circ$, how much is the value of $\angle DBC$?
In the figure (not drawn to scale) given below, if $AD = CD = BC$ and $\angle DBC = 96^\circ$, how much is the value of $\angle DBC$?
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For isosceles triangles, use the angle sum property and symmetry to calculate the base angles.
Updated On: Mar 23, 2026
- 32$^\circ$
- 84$^\circ$
- 64$^\circ$
- Cannot be determined
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The Correct Option is C
Solution and Explanation
Given that $AD = CD = BC$ and $\angle DBC = 96^\circ$, the triangle is isosceles, and the base angles are equal. We can calculate the value of $\angle DBC$ using the properties of isosceles triangles and angle sum of a triangle.
The base angles of $\triangle BCD$ are:
\[
\angle DBC = \frac{180^\circ - 96^\circ}{2} = 64^\circ
\]
Thus, the value of $\angle DBC$ is 64$^\circ$.
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