Question

find the value of w in rhombus efgh.\
angle at h: 10w - 20°\
angle at g: 6w + 88°\
find w.

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(10w - 20) + (6w + 88) = 180$$

Step2: Combine like terms

Simplify the left-hand side:
$$16w + 68 = 180$$

Step3: Isolate the variable term

Subtract 68 from both sides:
$$16w = 180 - 68$$
$$16w = 112$$

Step4: Solve for w

Divide both sides by 16:
$$w = \frac{112}{16}$$

Answer:

$7$