1.

ABCD is a square, BA=BQ, QRC and BPD are straight lines and ∠PBQ = 21°. Then, ∠BAQ equals(a) 60° (b) 84° (c) 78° (d) 74.5°

Answer»

(c) 78°

Since the diagonal of a square bisects the angle at the vertices, ∠DBC = 45°. 

∴ ∠ ABQ = 90° – (21° + 45°) 

= 90° – 66° = 24° 

In ΔBAQ, BA = BQ 

⇒ ∠BQA = ∠BAQ         (isos. Δ property)

∴ ∠BAQ = \(\frac{180°-24°}{2}=\frac{156°}{2}\) = 78°.



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