Question

what is ( mangle 1 )?

Explanation:

Step1: Find the measure of ∠BDC

Since ∠BDC and the \(130^{\circ}\) angle are supplementary (they form a linear pair), we use the formula \(m\angle BDC = 180^{\circ}-130^{\circ}\).
\(m\angle BDC=50^{\circ}\)

Step2: Use the triangle - angle sum property

In \(\triangle BDC\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle2\) be the unknown angle. Using the formula \(m\angle1 + m\angle2+m\angle BDC + m\angle C= 180^{\circ}\) (but since \(\angle1\) and \(\angle2\) form a linear pair with the angles of the triangle, we can also use the exterior - angle related approach. Another way: since \(m\angle ABD = 180^{\circ}\) (a straight line), and we know from the triangle \(\triangle BDC\) (where \(m\angle BDC = 50^{\circ}\), \(m\angle C=70^{\circ}\)), then \(m\angle2=180^{\circ}-(50^{\circ} + 70^{\circ})=60^{\circ}\). And since \(m\angle1+m\angle2 = 180^{\circ}\) (linear pair), \(m\angle1=180^{\circ}-m\angle2\).
\(m\angle1 = 120^{\circ}\)

Answer:

D. \(120^{\circ}\)