Question

1 m∠c = 72° given try m∠cde = 54° select a reason select a reason vertical angles linear pair (or triple) congruent angles sum of angles in a triangle sum of angles in a quadrilateral base angle of an isosceles triangle angle bisector definition corresponding angles alternate interior angles alternate exterior angles same - side interior angles angle addition postulate angle subtraction postulate perpendicular lines form right angles

Explanation:

Step1: Recall the sum of angles in a triangle

In a triangle, the sum of the interior angles is \(180^{\circ}\).

Step2: Assume the triangle is isosceles (if applicable)

If the triangle has two equal sides (not shown in the problem but if we assume based on common problems of this type where angle \(C = 72^{\circ}\) and we are finding another angle in a triangle - like maybe a triangle with two equal sides). Let's assume it's an isosceles triangle. But wait, no, if we consider the formula for the sum of angles in a triangle. Wait, no, maybe there is a right - angle assumption missing. Wait, no, the problem is incomplete in terms of figure details. But if we assume it's a triangle - related problem (since the options have sum of angles in a triangle). Let's assume it's a triangle where we know one angle \(C = 72^{\circ}\) and maybe another angle (if it's a right - triangle, but \(54+72 = 126
eq90\)). Wait, no, if we use the sum of angles in a triangle formula \(A + B+C=180^{\circ}\). But since we have only two angles shown (\(C = 72^{\circ}\) and \(\angle CDE=54^{\circ}\)), maybe it's a case of a triangle where we use the sum of angles. But wait, no, the most likely reason is that if we assume it's a triangle and we use the sum of angles in a triangle. Wait, no, another approach: if we consider that in a triangle, if we know two angles, we can find the third. But here we are given one angle \(C = 72^{\circ}\) and the answer \(\angle CDE = 54^{\circ}\). If we assume it's a triangle and we use the formula \(180-(90 + 36)\) no. Wait, no, if we consider the reason as sum of angles in a triangle. Let’s assume that in a triangle, if we have two angles: say if it's a triangle with angles \(x\), \(y\), \(z\) and \(x + y+z=180^{\circ}\). But since we have \(m\angle C = 72^{\circ}\) and \(m\angle CDE = 54^{\circ}\), maybe there is a right - angle (assumed \(90^{\circ}\) missing in problem description). Wait \(72 + 54+54=180\) (if it's an isosceles triangle with two angles of \(54^{\circ}\)). But the reason from the list: the sum of angles in a triangle formula \(A + B + C=180^{\circ}\).

Answer:

Sum of angles in a triangle