Question
Download Solution PDFIn the given figure, AB = DB and AC = DC. If ∠ABD = 58° and ∠DBC = (2x - 4)°, ∠ACB = (y + 15)° and ∠DCB = 63°, then the value of 2x + 5y is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB = DB and AC = DC.
∠ABD = 58° and ∠DBC = (2x - 4)°,
∠ACB = (y + 15)° and ∠DCB = 63°
Concept used:
If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS (Side - Side - Side) rule.
Calculation:
As AB = DB, AC = DC, and BC is common for two triangle
So, ΔABC ≅ ΔDBC
So, ∠ABC = ∠DBC = ∠ABD/2
⇒ 58°/2 = 29°
So,
(2x - 4)° = 29°
⇒ 2x = 33°
Again,
∠ACB = ∠DCB = 63°
So,
(y + 15)° = 63°
⇒ y = 48°
So,
2x + 5y = 33° + 5 × 48°
⇒ 33° + 240°
⇒ 273°
∴ The required answer is 273°.
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