Question
Download Solution PDFIn the given triangle, CD is the bisector of ∠BCA. CD = DA. If ∠BDC = 76°, What is the degree measure of ∠CBD?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
CD is the bisector of ∠BCA.
CD = DA
∠BDC = 76°
Concept Used:
The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.
Angle Sum Property = Sum of all the three angles of a triangle is 180°.
Calculation:
In triangle ABC,
CD is the bisector of ∠BCA.
⇒ ∠BCD = ∠DCA = θ
Since, CD = DA [Given]
⇒ ∠DCA = ∠CAD = θ
⇒ ∠BDC = 76° [Given]
⇒ ∠BDC = ∠DCA + ∠CAD
⇒ θ + θ = 76°
⇒ 2θ = 76°
⇒ θ = 38°
In triangle CBD,
∠BCD + ∠CDB + ∠CBD = 180°
⇒ θ + 76° + ∠CBD = 180°
⇒ 38° + 76° + ∠CBD = 180°
⇒ ∠CBD = 180° - 114°
⇒ ∠CBD = 66°
∴ Option 4 is the correct answer.
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