Question

7.
10
39°
36°
15
a=
b=
x=
y=

Explanation:

Step1: Find \(a\) and \(b\)

In a parallelogram, opposite sides are equal.
So, \(a = 10\) and \(b=15\)

Step2: Find \(x\)

Since the figure is a parallelogram, alternate - interior angles are equal.
\(x = 36^{\circ}\)

Step3: Find \(y\)

We know that in a parallelogram, the sum of adjacent angles is \(180^{\circ}\). Also, using the angle - sum property of a triangle.
First, the angle adjacent to \(39^{\circ}+36^{\circ}\) in the triangle: \(\angle=39^{\circ}\) (alternate - interior angles in parallelogram)
In a triangle, using the angle - sum property (\(180^{\circ}\)), \(y=180-(39 + 36+39)=66^{\circ}\)

Answer:

\(a = 10\), \(b = 15\), \(x = 36^{\circ}\), \(y = 66^{\circ}\)