Given AB//CD, angle CEF = 5a + 40° and EF B = a + 100°. What is the value of a? State reasons for you answer.

Here's a step-by-step solution for the given problems. Question 7.1 Step 1: Identify the relationship between the angles. Angles CEF and EFB are consecutive interior angles (also known as co-interior angles) because they are between the parallel lines AB and CD and on the same side of the transversal line EF. When two parallel lines are intersected by a transversal, consecutive interior angles are supplementary, meaning their sum is 180^. Step 2: Set up the equation and solve for a. CEF + EFB = 180^ (5a + 40^) + (a + 100^) = 180^ 6a + 140^ = 180^ 6a = 180^ - 140^ 6a = 40^ a = (40)/(6) a = (20)/(3) The value of a is (20)/(3). Question 7.2 Given TS PR. We need to find the values of a, b, and c. From the diagram: c = SQR a = QSR b = SRQ Step 1: Find the value of c. Angles PQR and SQR are angles on a straight line PQR. Therefore, their sum is 180^. PQR + SQR = 180^ 154^ + c = 180^ c = 180^ - 154^ c = 26^ Step 2: Find the value of TSQ. Since TS PR and SQ is a transversal, TSQ and SQR are alternate interior angles. TSQ = SQR TSQ = c TSQ = 26^ Step 3: Relate a and b using parallel lines. Since TS PR and SR is a transversal, TSR and SRQ are alternate interior angles. TSR = SRQ From the diagram, TSR = TSQ + QSR. TSR = 26^ + a So, we have the equation: b = 26^ + a (1) Step 4: Use the sum of angles in SQR. The sum of angles in a triangle is 180^. QSR + SRQ + SQR = 180^ a + b + c = 180^ Substitute the value of c = 26^: a + b + 26^ = 180^ a + b = 180^ - 26^ a + b = 154^ (2) Step 5: Solve the system of equations for a and b. Substitute equation (1) into equation (2): a + (26^ + a) = 154^ 2a + 26^ = 154^ 2a = 154^ - 26^ 2a = 128^ a = (128^)/(2) a = 64^ Now substitute the value of a back into equation (1) to find b: b = 26^ + 64^ b = 90^ The values are: a = 64^ b = 90^ c = 26^ Send me the next one 📸