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

March 22, 2026Mathematics

ScanSolve AI Answer

March 22, 2026

Part (a): Finding $x$

Step 1: The sum of the interior angles in a triangle is $180^\circ$ .

\sum angles = 180^\circ

Step 2: Substitute the known angles.

18^\circ + 20^\circ + x = 180^\circ

Step 3: Simplify the left side.

38^\circ + x = 180^\circ

Step 4: Solve for $x$ .

x = 180^\circ - 38^\circ = 142^\circ

So, $x = \mathbf{142^\circ}$

142^\circ

Part (b): Finding $b$

Step 1: Adjacent angles on a straight line sum to $180^\circ$ .

adjacent angles sum = 180^\circ

Step 2: Substitute the known angle.

130^\circ + b = 180^\circ

Step 3: Solve for $b$ .

b = 180^\circ - 130^\circ = 50^\circ

So, $b = \mathbf{50^\circ}$

50^\circ

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