1. **Problem Statement:** Given a geometric figure with angles labeled Q, Z, R, B, E, and others, solve for the following: ক) Find $Z$ if $Q = 75^\circ$. খ) Determine the values of $R$ and $Q$. গ) Prove that $\angle B + \angle E = 360^\circ$. ঘ) Find how many angles are formed in the figure. 2. **Important Rules and Formulas:** - The sum of angles around a point is $360^\circ$. - The sum of angles in a triangle is $180^\circ$. - Vertically opposite angles are equal. - Adjacent angles on a straight line sum to $180^\circ$. 3. **Solution for (ক):** - Given $Q = 75^\circ$. - Since $Q$ and $Z$ are adjacent angles on a straight line, they sum to $180^\circ$. - Therefore, $$Z = 180^\circ - Q = 180^\circ - 75^\circ = 105^\circ.$$ 4. **Solution for (খ):** - $Q$ is given as $75^\circ$. - To find $R$, observe the figure relationships (assuming $R$ and $Q$ are vertically opposite or supplementary angles). - If $R$ and $Q$ are vertically opposite, then $$R = Q = 75^\circ.$$ - If $R$ and $Q$ are supplementary, then $$R = 180^\circ - Q = 105^\circ.$$ - Without additional information, the most common assumption is vertically opposite angles are equal, so $R = 75^\circ$. 5. **Solution for (গ):** - To prove $\angle B + \angle E = 360^\circ$. - Angles $B$ and $E$ are likely angles around a point or forming a full rotation. - By the rule, the sum of angles around a point is $360^\circ$. - Therefore, $$\angle B + \angle E = 360^\circ.$$ 6. **Solution for (ঘ):** - Count the number of angles formed in the figure. - From the labels, angles are $L, R, A, Z, Q, S, x, B, P, C, E, D, M, y$. - Total distinct angles = 14. 7. **Inconsistencies Noted:** - The problem does not provide a clear figure or relationships between all angles. - Some angles like $x, y, S, M$ are mentioned but not defined. - Without a diagram, assumptions are made based on common geometric rules. **Final Answers:** - ক) $Z = 105^\circ$ - খ) $R = 75^\circ$, $Q = 75^\circ$ - গ) $\angle B + \angle E = 360^\circ$ - ঘ) Number of angles formed = 14