A sector of a circle having a radius 14 cm has area 154 cm². Find the angle of the sector.
90°
Step 1 – Sector area formula:
\(A = \dfrac{\theta}{360^{\circ}} \times \pi r^{2}\)
Step 2 – Substitute given values (using π = 22/7):
\(154 = \dfrac{\theta}{360} \times \dfrac{22}{7} \times 14^{2} = \dfrac{\theta}{360} \times \dfrac{22}{7} \times 196\)
\(154 = \dfrac{\theta}{360} \times 616\)
Step 3 – Solve for θ:
\(\dfrac{\theta}{360} = \dfrac{154}{616} = \dfrac{1}{4} \;\Rightarrow\; \theta = 90^{\circ}\)
Hence the angle of the sector is 90°.
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