Question

1. △abd≌△cdb. find x. 5. △wxv≌△zyv. find a.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle WXV\cong\triangle ZYV\), corresponding angles are equal.

Step2: Apply the angle - sum property of a triangle

In \(\triangle WXV\), we know that the sum of angles in a triangle is \(180^{\circ}\). Let \(a\) be the angle we want to find. We know one angle is \(52^{\circ}\) and the vertical - angle (opposite to the \(84^{\circ}\) angle in the other part of the figure) is \(84^{\circ}\). Using the formula \(a + 52^{\circ}+(180 - 84)^{\circ}=180^{\circ}\) (because the non - congruent part of the angle at the intersection is \(180 - 84\) due to linear pair).
Another way: Since \(\triangle WXV\cong\triangle ZYV\), \(\angle WXV=\angle ZYV\), \(\angle XVW=\angle YVZ\). We know that \(\angle XVW = 180 - 84=96^{\circ}\) (linear pair). Then \(a=180-(52 + 96)\)

$$a=180-(52 + 96)=180 - 148 = 32^{\circ}$$

Answer:

\(32^{\circ}\)