The figure given below, shows a circle with centre O. Given: ∠ AOC = a and ∠ ABC = b.
1. Find the relationship between a and b.
2. Find the measure of angle OAB, if OABC is a parallelogram.
1. Find the relationship between a and b.
2. Find the measure of angle OAB, if OABC is a parallelogram.
Exercise 17 (A) | Q 23 | Page 259
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(i) $\angle ABC =\frac{1}{2}$ Reflex $( COA )$
(Angle at the centre is double the angle at the circumference subtended by the same chord)
$\Rightarrow b=\frac{1}{2}(360-a)$
⇒ a + 2b = 360°
(ii) Since OABC is a parallelogram, so opposite angles are equal.
2b + b = 360°
3b = 360°
b = 120°
∴ 120° + 120° + x + x = 360°
2x = 360° - 240°
2x = 120°
$x=\frac{120^{\circ}}{2}$
$x=60^{\circ}$
$\Rightarrow \angle O A B=60^{\circ}$
(Angle at the centre is double the angle at the circumference subtended by the same chord)
$\Rightarrow b=\frac{1}{2}(360-a)$
⇒ a + 2b = 360°
(ii) Since OABC is a parallelogram, so opposite angles are equal.
2b + b = 360°
3b = 360°
b = 120°
∴ 120° + 120° + x + x = 360°
2x = 360° - 240°
2x = 120°
$x=\frac{120^{\circ}}{2}$
$x=60^{\circ}$
$\Rightarrow \angle O A B=60^{\circ}$
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