A decorative HDB tile is shaped as a rhombus $ABCD$. The angle at vertex $A$ is $(3x + 10)°$ and the angle at the OPPOSITE vertex $C$ is $(5x - 30)°$. Find the value of $x$.
Show Worked Solution
Worked Solution
Step 1: Identify the property. In a rhombus, OPPOSITE angles are EQUAL. ∠A and ∠C are opposite angles, so $\angle A = \angle C$.\n
Step 2: Set up the equation: $3x + 10 = 5x - 30$.\n
Step 3: Move x-terms to one side and constants to the other: $10 + 30 = 5x - 3x$, which gives $40 = 2x$.\n
Step 4: Solve: $x = 40 \div 2 = 20$.\nCheck: $\angle A = 3(20) + 10 = 70°$ and $\angle C = 5(20) - 30 = 70°$. Equal ✓. (And $\angle B = \angle D = 180° - 70° = 110°$ as consecutive angles in a rhombus are supplementary.)
Answer: 20
Correct answer: 20
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free