Question

Given that AB is a line segment and the angle y = 47°, work out the value of the angle marked x.

The diagram is not drawn to scale.

Please answer..

Answer 1

`\huge\boxed{\bf\:x^(\circ) = 133^(\circ)}`

Explanation:

From the given figure, we can see that the 2 pairs of angles, x° & y° form a linear pair where they're sum will be 180°.

In line segment AB, it's given that y = 47°. This means that,

`\sf\:x^(\circ) + y^(\circ) = 180^(\circ)\\\sf\:x^(\circ) + 47^(\circ) = 180^(\circ)\\\sf\:x^(\circ) = 180^(\circ) - 47^(\circ)\\\boxed{\bf\:x^(\circ) = 133^(\circ)}`

•°• The value of the angle marked as x = 133°

`\rule{150}{2}`

Some Key Definitions:

Linear Pair:

• A pair of angles that make a straight line. If they make a straight line then their angle will be 180° .

Supplementary Angles:

• Angles that sum up to 180°. A linear pair forms supplementary angles.

180° :

• The exact half of a full angle (360°).
• 360/2 = 180
• 180° is also known as a srraight angle.

`\rule{150}{2}`

Answer 2

x = 133°

Explanation:

Straight-line pair - A pair of angles that lie on a straight line.

*Property*

The sum of two angles of a straight-line pair is equal to 180°.

The given angles – x and y – form a straight-line pair.

==> x + y = 180

{y = 47° (given in the question)}

Substituting 47 for y:

==> x + 47 = 180

Subtracting 47 from both sides:

==> x = 47 - 47 = 180 - 47

==> x = 133