Question : If $\cos3A = \sin (A-18°)$, where 3A is an acute angle, what is the value of A?

Option 1: 110°

Option 2: 108°

Option 3: 54°

Option 4: 27°

Question : If $\tan 2 \theta=\cot \left(\theta-36^{\circ}\right)$, where $2 \theta$ is an acute angle, then the value of $\theta$ is:

Option 1: 18°

Option 2: 36°

Option 3: 30°

Option 4: 42°

Question : In a cyclic quadrilateral MNOP, $\angle$M is opposite to $\angle$O, If 2$\angle$O = 3$ \angle$M, then what is the value of $\angle$M?

Option 1: 88°

Option 2: 108°

Option 3: 72°

Option 4: 96°

Question : If $\sin A=\frac{2}{5}$, where $A$ is an acute angle, what is the value of $\frac{5 \sin A+2 \operatorname{cosec} A}{\sqrt{21} \sec A}$?

Option 1: $\frac{5}{4}$

Option 2: $\frac{7}{5}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{5}{7}$

Question : In a $\triangle ABC$, $\angle A +\angle B=70°$ and $\angle B+\angle C=130°$.Then, the value of $\angle A$ is:

Option 1: 20°

Option 2: 50°

Option 3: 80°

Option 4: 200°

Question : If A, B, and C are the acute angles, such that $\tan (A+B-C)=\frac{1}{\sqrt{3}}, ~\cos (B+C-A)=\frac{1}{2},$ and $\sin (C+A-B)=\frac{1}{\sqrt{2}}$. The value of A + B + C will be equal to:

Option 1: 90°

Option 2: 110°

Option 3: 170°

Option 4: 135°