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Find the value of the angles marked with letters in the following figures.

March 22, 2026Mathematics

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Answers

2 parts

142^\circ

50^\circ

7 steps

Finding $x$

The sum of the interior angles in a triangle is $180^\circ$ .
$\sum \text{angles} = 180^\circ$
Substitute the known angles.
$18^\circ + 20^\circ + x = 180^\circ$
Simplify the left side.
$38^\circ + x = 180^\circ$
Solve for $x$ .
$x = 180^\circ - 38^\circ = 142^\circ$
So, $x = \mathbf{142^\circ}$

142^\circ

Finding $b$

Adjacent angles on a straight line sum to $180^\circ$ .
$\text{adjacent angles sum} = 180^\circ$
Substitute the known angle.
$130^\circ + b = 180^\circ$
Solve for $b$ .
$b = 180^\circ - 130^\circ = 50^\circ$
So, $b = \mathbf{50^\circ}$

50^\circ

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