Question

find d in the figure. (1 point)

Explanation:

Step1: Find the third - angle of the triangle

The sum of interior angles of a triangle is \(180^{\circ}\). Let the third - angle of the triangle be \(x\). We know two angles: one is \(50^{\circ}\) and the other is \(180 - 70=110^{\circ}\) (since the adjacent angle to \(70^{\circ}\) inside the triangle forms a linear pair). Using the formula \(x + 50+(180 - 70)=180\), we can also use another way. The sum of interior angles of a triangle \(A + B + C=180^{\circ}\). Let the two known interior angles of the triangle be \(A = 50^{\circ}\) and \(B=70^{\circ}\) (the non - adjacent interior angle to \(d\)). Then the third interior angle \(C=180-(50 + 70)=60^{\circ}\).

Step2: Use the linear - pair relationship

Since \(c\) and \(d\) form a linear pair (\(c + d=180^{\circ}\)), and \(c\) is an interior angle of the triangle. Also, using the exterior - angle property: The exterior angle \(d\) of a triangle is equal to the sum of the two non - adjacent interior angles. The two non - adjacent interior angles to \(d\) are \(50^{\circ}\) and \(70^{\circ}\).
So \(d=50 + 70\)

Answer:

\(120\)