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


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Given That AB Is A Line Segment And The Angle Y 47 Work Out The Value Of The Angle Marked XThe Diagram Is Not Drawn To ScalePlease Answer class=

Answer :

Answer:

x = 133°

Step-by-step 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

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Answer:

[tex]\huge\boxed{\bf\:x^{\circ} = 133^{\circ}}[/tex]

Step-by-step 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,

[tex]\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}}[/tex]

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

[tex]\rule{150}{2}[/tex]

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.

[tex]\rule{150}{2}[/tex]

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