ABCD is a rectangle.angle b is 1/2 of angle a.angle b is 2/3 of angle c find angle c
Answer (1)
Answer:1. Understand Rectangle Properties: - In a rectangle, opposite angles are equal. Therefore, ∠A = ∠C and ∠B = ∠D.- Adjacent angles are supplementary (add up to 180°). Therefore, ∠A + ∠B = 180°. 2. Set up Equations: - We are given that ∠B = (1/2)∠A.- We are also given that ∠B = (2/3)∠C.- Since ∠A = ∠C, we can substitute ∠C for ∠A in the first equation: ∠B = (1/2)∠C 3. Solve for Angle C: Since both expressions equal ∠B, we can set them equal to each other: (1/2)∠C = (2/3)∠C Now solve for ∠C: Multiply both sides by 6 to eliminate fractions: 3∠C = 4∠C Subtract 3∠C from both sides: 0 = ∠C
