In a quadrilateral ABCD, AB = BC, AD = DC. ∠ABD = 68°, ∠ADB = (2y - 7)°, ∠BDC = 33°, ∠DBC = (3x + 2)°. Then the value of 2x + 3y is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 104°.
It is clear from the diagram that ΔBAD ≅ ΔBCD {By side angle side}
So, ∠ABD = ∠CBD and ∠ADB = ∠CDB
Now,
∠ABD = ∠CBD
⇒ 68° = 3x + 2
⇒ x = 22°
∠ADB = ∠CDB
⇒ 2y - 7 = 33°
⇒ y = 20°
So, 2x + 3y = 2 × 22° + 3 × 20°
⇒ 44° + 60°
⇒ 104°