Question

135° and x + 40° (from the hand - drawn geometric figure on lined paper)

Explanation:

To solve for \( x \), we assume this is a problem involving the exterior angle of a triangle or supplementary angles (since the diagram likely shows a triangle with an exterior angle). If we consider the relationship between the interior angle (\( 135^\circ \)) and the exterior angle (\( x + 40^\circ \)):

Step 1: Recall the property of supplementary angles or exterior angles

If the \( 135^\circ \) angle and the angle adjacent to \( x + 40^\circ \) are supplementary (or if \( x + 40^\circ \) is an exterior angle equal to the remote interior angle), we use the fact that:
\( x + 40^\circ = 135^\circ \) (assuming the exterior angle equals the non - adjacent interior angle, or supplementary angle relationship simplifies to this).

Step 2: Solve for \( x \)

Subtract \( 40^\circ \) from both sides of the equation:
\( x = 135^\circ - 40^\circ \)
\( x = 95^\circ \)

Answer:

\( x = 95^\circ \)