Question

In the following diagram,

start overline, H, I, end overline is parallel to

start overline, J, K, end overline.

Answer 1

Keys

• Parallel Lines

They have the same measure of corresponding angles.

Solution

If we find the remaining angles in the triangle,

$\angle AIH=180^{\circ}-(56+66)^{\circ}=58^{\circ}$

It is a corresponding angle for $\angle x$. So,

$\angle x=58^{\circ}$

More information

Corresponding angles mean the angles in the same places.

Alternative angles mean the angles in opposite places.

Answer 2

Answer:

• Value of x = 58°.

Step-by-step explanation:

Given:

• HI is parallel to JK.
• ∠H = 56°
• ∠A = 66°

To Find:

• ∠k or x.

What is Parallel lines with a transversal?

• So, transversal is a line that intersect two or more parallel lines. When two or more line cut by transversal then the angle formed are same are called as corresponding angle.

In ΔIAH

⇒ ∠I + ∠A + ∠H = 180°  (Angle sum property)

⇒ ∠I + 66° + 56° = 180°

⇒ ∠I + 122° = 180°

⇒ ∠I = 180° - 122°

⇒ ∠I = 58°

So, ∠k or x = 58°  (Corresponding angle)

Hence, value of x = 58°.