Question

question 11 (multiple choice worth 4 points)
(02.08h mc)
figure abcd is a rhombus where m∠abc = 84° and m∠abe = 3x - 6. solve for x.
image of rhombus abcd with diagonals intersecting at e
options:
16
30
32
62
question 12 (multiple choice worth 4 points)
(02.08h mc)

Explanation:

Step1: Identify angle relationship

In a rhombus, diagonals bisect the angles, so $m\angle ABE = \frac{1}{2}m\angle ABC$.

Step2: Substitute given values

Substitute $m\angle ABC=84^\circ$ and $m\angle ABE=3x-6$:
$$3x - 6 = \frac{1}{2} \times 84$$

Step3: Simplify right-hand side

Calculate the right-hand side:
$$3x - 6 = 42$$

Step4: Solve for x

Add 6 to both sides, then divide by 3:
$$3x = 42 + 6 = 48$$
$$x = \frac{48}{3} = 16$$

Answer:

16