Question

lines ef and gh and ray jk intersect at point j. for each of the angles without an angle measure, place the drawing.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle vertical to the $67^{\circ}$ angle has a measure of $67^{\circ}$.

Step2: Find supplementary angles

The angle adjacent to the $67^{\circ}$ angle on the line $GH$ forms a linear - pair. A linear - pair of angles is supplementary (sum to $180^{\circ}$). Let the unknown adjacent angle be $x$. Then $x + 67^{\circ}=180^{\circ}$, so $x = 180^{\circ}-67^{\circ}=113^{\circ}$. The vertical angle to this $113^{\circ}$ angle also has a measure of $113^{\circ}$.

Step3: Consider right - angles

Since $EF$ and $JK$ are perpendicular, the four angles formed at their intersection are right - angles, each with a measure of $90^{\circ}$.

Answer:

The angles with measures: two angles of $67^{\circ}$, two angles of $113^{\circ}$, and four angles of $90^{\circ}$ should be placed in the drawing according to the vertical - angle and linear - pair relationships.