This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here's the solution to question 6.1: 6.1.1 Name three other angles, with reasons, equal to 32^. Given B = KBA = 32^. 1. Angle: KTA Reason: Angles in the same segment (subtended by arc KA) are equal. KTA = KBA = 32^ 2. Angle: KCA Reason: Angles in the same segment (subtended by arc KA) are equal. KCA = KBA = 32^ 3. Angle: NAC Reason: Given CN = NA, CNA is an isosceles triangle. The base angles opposite the equal sides are equal. Since KCA = 32^, then NCA = 32^. Therefore, NAC = NCA. NAC = 32^ 6.1.2 Determine the values of the following: 6.1.2a) M Assuming M refers to KMA, the angle at the center. Step 1: Identify the relationship between the angle at the center and the angle at the circumference. The angle at the center subtended by an arc is twice the angle at the circumference subtended by the same arc. Arc KA subtends KMA at the center and KBA at the circumference. Step 2: Calculate the angle. KMA = 2 × KBA KMA = 2 × 32^ KMA = 64^ The value of M is 64^ 6.1.2b) T_1 T_1 refers to KTA. Step 1: Identify the relationship between KTA and KBA. Both angles are subtended by the same arc KA in the circle. Step 2: State the value. KTA = KBA KTA = 32^ The value of T_1 is 32^ 6.1.2c) N N refers to CNA. Step 1: Use the given information about CNA. We are given CN = NA, which means CNA is an isosceles triangle. Step 2: Determine the base angles of CNA. From 6.1.1, we found NCA = 32^ and NAC = 32^. Step 3: Calculate CNA using the sum of angles in a triangle. The sum of angles in CNA is 180^. CNA + NAC + NCA = 180^ CNA + 32^ + 32^ = 180^ CNA + 64^ = 180^ CNA = 180^ - 64^ CNA = 116^ The value of N is 116^ That's 2 down. 3 left today — send the next one.