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In the diagram below, determine the value of x:

In the diagram below, determine the value of x:-example-1
User MichaelD
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1 Answer

5 votes

9514 1404 393

Answer:

55°

Explanation:

130° is an external angle to the small triangle at lower left, so is the sum of the remote interior angles. The unmarked interior angle at the bottom of that triangle is then 130° -30 = 100°.

That is an exterior angle of the large triangle that has remote interior angles of 45° and x°. So, ...

x° + 45° = 100°

x° = 100° -45°

x° = 55°

_____

Alternate solution

The sum of the interior angles of a quadrilateral is 360°. Three of the angles in the bounding quadrilateral are x°, 45°, 30°. The fourth is the reflex angle that is (360° -130°) = 230°. So, we have ...

x° +45° +230° +30° = 360° . . . . . angles CCW from lower right

x° = 360° -305°

x° = 55°

User John Fischer
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