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.
ScanSolve AI Answer
Step 1: Prove that opposite sides of parallelogram PQRS are equal. Given that PQRS is a parallelogram, we know that PQ RS and PR QS. Draw a diagonal PS. Consider PQS and RSP: • QPS = RSP (Alternate interior angles, since PQ RS) • QSP = RPS (Alternate interior angles, since PR QS) • PS = SP (Common side) Therefore, PQS RSP (Angle-Side-Angle congruence criterion). Since the triangles are congruent, their corresponding sides are equal: • PQ = RS • QS = PR Thus, the opposite sides of the parallelogram are equal. Step 2: Calculate the value of x for parallelogram EFGH. In a parallelogram, consecutive angles are supplementary. Therefore, G + F = 180^. Substitute the given expressions for G and F: (9x + 12^) + (15x - 24^) = 180^ 24x - 12^ = 180^ 24x = 180^ + 12^ 24x = 192^ x = (192)/(24) x = 8 The value of x is 8. Step 3: Determine the size of E. In a parallelogram, opposite angles are equal. Therefore, E = G. First, calculate the measure of G using the value of x found in Step 2: G = 9x + 12^ G = 9(8) + 12^ G = 72^ + 12^ G = 84^ Since E = G: E = 84^ The size of E is 84^. Send me the next one 📸