1. **Find the unknown marked angle in each triangle.** The sum of angles in any triangle is always $180^\circ$. 2. **Calculate the value of each variable.** Use the fact that the sum of angles in a triangle is $180^\circ$ and apply algebraic equations. 3. **Show that $\angle A + \angle B + \angle C + \angle D + \angle E + \angle F = 360^\circ$.** This is a property of the angles around a point or in a star figure. 4. **Find $\angle BOC$ and $\angle OBC$ given bisectors and angles.** Use angle bisector properties and triangle angle sum. 5. **Find the angles of a triangle with ratio 2:3:4.** Set angles as $2x$, $3x$, $4x$ and solve $2x+3x+4x=180$. 6. **Determine which groups of angles cannot form a triangle.** Check if the sum equals $180^\circ$. 7. **Find angles of a triangle with two equal angles each twice the third.** Set the third angle as $x$, equal angles as $2x$, solve $x+2x+2x=180$. **Step-by-step solution for the first problem only:** 1. The problem: Find the unknown angle in each triangle given two angles. 2. Formula: Sum of angles in a triangle is $180^\circ$. 3. For each triangle, unknown angle $= 180^\circ - (\text{sum of given angles})$. 4. Calculate: (a) $180 - (63 + 70) = 180 - 133 = 47^\circ$ (b) $180 - (49 + 40) = 180 - 89 = 91^\circ$ (c) $180 - (20 + 125) = 180 - 145 = 35^\circ$ (d) $180 - (48 + 84) = 180 - 132 = 48^\circ$ (e) $180 - (60 + 45) = 180 - 105 = 75^\circ$ (f) Only one angle given $45^\circ$, so unknown angles cannot be found without more info. (g) Sum of given angles $37 + 28 + 108 = 173^\circ$, which is more than $180^\circ$, so this is not a triangle. (h) Sum of given angles $100 + 65 + 45 + 40 = 250^\circ$, plus unknown $q$, which cannot be a triangle. **Final answers for (a) to (e):** (a) $47^\circ$ (b) $91^\circ$ (c) $35^\circ$ (d) $48^\circ$ (e) $75^\circ$ **Slug:** unknown angles **Subject:** geometry **Desmos:** {"latex":"y=0","features":{"intercepts":true,"extrema":true}} **q_count:** 8