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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Fresh day Oliverkoome@gmail254.Com., let's solve. 7. In the given figure, A, B, C, D, and E are points on the circumference of the circle. Line AB is parallel to line DC and line FAG is tangent to the circle at A. Angle GAB = 25^ and angle ABC = 100^. a) Determine the size of BAC. Step 1: Identify the cyclic quadrilateral ABCD. The sum of opposite angles in a cyclic quadrilateral is 180^. ADC + ABC = 180^ Given ABC = 100^: ADC + 100^ = 180^ ADC = 180^ - 100^ ADC = 80^ Step 2: Apply the Tangent-Chord Theorem. The angle between the tangent FAG and chord AC ( GAC) is equal to the angle in the alternate segment ( ADC). GAC = ADC GAC = 80^ Step 3: From the figure, GAC is the sum of GAB and BAC. GAC = GAB + BAC Given GAB = 25^: 80^ = 25^ + BAC BAC = 80^ - 25^ BAC = 55^ The size of BAC is: 55^ b) Determine the size of AED. Step 1: Use the property of parallel lines. Since AB is parallel to DC, and AC is a transversal, the alternate interior angles are equal. BAC = ACD From part (a), BAC = 55^: ACD = 55^ Step 2: Apply the property of angles subtended by the same arc. Angles subtended by the same arc at the circumference are equal. Both AED and ACD subtend arc AD. AED = ACD AED = 55^ The size of AED is: 55^ Send me the next one 📸