Question

solve for the missing angle.
d

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So the sum of angles in the two triangles is related. The sum of angles in a triangle is \(180^{\circ}\). Let the missing angle be \(x\).
For the lower - triangle: the third angle (vertical to the angle in the upper - triangle) is \(180^{\circ}-(20^{\circ} + 40^{\circ})\).
For the upper - triangle: \(180^{\circ}=39^{\circ}+x+(180^{\circ}-(20^{\circ}+40^{\circ}))\).
Another way: Since vertical angles are equal, we can use the angle - sum property of triangles directly.
We know that \(x + 39^{\circ}=20^{\circ}+40^{\circ}\) (because the non - vertical angles of the two triangles are related by the vertical - angle equality and angle - sum of triangles (\(180^{\circ}\) for each triangle, so \(180^{\circ}-(\text{vertical angle})-x=180^{\circ}-(\text{vertical angle})-(20^{\circ} + 40^{\circ})\)).

Step2: Solve for \(x\)

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Answer:

\(21^{\circ}\)