Answer:
135°
10
Step-by-step explanation:
Quadrilateral EFGH is a parallelogram, In order to solve the give question, we should have the idea of some properties of the parallelogram which are listed below.
- Opposite sides are equal in measure.
- Consecutive angles are supplementay.
- Measures of opposite angles are equal.
Let us apply the above properties and work out the given question.
[tex]\angle F + \angle G=180\degree \\ (consecutive \: \angle s) \\ \\ \implies \: (3x - 15) \degree + (7x - 5) \degree = 180 \degree \\ \\ \implies \: (3x - 15 + 7x - 5) \degree = 180 \degree \\ \\ \implies \: (10x - 20) \degree = 180 \degree \\ \\ \implies \: 10x - 20= 180 \\ \\ \implies \: 10x = 180 + 20 \\ \\ \implies \: 10x = 200 \\ \\ \implies \: x = \frac{200}{10} \\ \\ \implies \: \blue{\bold{x = 20}} \\ \\ m\angle E= m\angle G \\ (opposite \: angles \: of \: parallelogram) \\ \\ \implies \: m\angle E=(7x - 5) \degree = (7 \times 20 - 5) \degree = (140 - 5) \degree\\ \\\implies \: \huge \red{m\angle E= \boxed{135} \degree} \\ \\ EF = HG \: \\ (opposite \: sides \: of \: parallelogram) \\ \implies \: 3y = y + 8 \\ \\ \implies \:3y - y = 8 \\ \\ \implies \:2y = 8 \\ \\ \implies \:\orange{\bold{y = 4}}\\\\FG = EH\\(opposite \: sides \: of \: parallelogram) \\ \\ \implies FG = 2(y + 1) = 2(4 + 1) = 2(5) \\ \\ \implies \huge\purple{ FG =\boxed{10}}[/tex]
