Question
In the given figure, $AB = AD ; CB = CD ; \angle A =42^{\circ}$ and $\angle C =108^{\circ}$, find $\angle ABC$.
✓
Answer
$105^{\circ}$
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One day three friends Amit (A), Binay (B) and Chanchal (C) were playing hide and seek game in the park of their society. Amit and Binay hide in the shrubs and Chanchal has to find both of them. If the position of three friends are at A, B and C respectively, as shown in the figure and forms a right angled triangle ABC such that AB = 6m, $B C=2 \sqrt{3} m$ and $\angle B =90$.
Based on the above information, answer the following questions :
Q.1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3} m$ (c) $5 \sqrt{3} m$ (d) $4 \sqrt{3} m$
Q.2. The measure of $\angle A$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.3. The measure of $\angle C$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.4. $\cos 2 A$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
Q.5. $2 \sin \left(\frac{ C }{2}\right)$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
→Based on the above information, answer the following questions :
Q.1. The length of AC is :
(a) 4 m (b) $8 \sqrt{3} m$ (c) $5 \sqrt{3} m$ (d) $4 \sqrt{3} m$
Q.2. The measure of $\angle A$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.3. The measure of $\angle C$ is :
(a) 30 (b) 45 (c) 60 (d) 90
Q.4. $\cos 2 A$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\frac{\sqrt{3}}{2}$ (d) $\sqrt{3}$
Q.5. $2 \sin \left(\frac{ C }{2}\right)$ is equal to :
(a) 1 (b) $\frac{1}{2}$ (c) $\sqrt{3}$ (d) $\frac{\sqrt{3}}{2}$
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