1. In the figure below, WPRT is square. QWU and SWV are straight lines. ∠QWP = 13° and ∠SWT = 28°. Find ∠UWV

WPRT is a square. A square has 4 equal sides and have 4 right angled corners. Hence, we know that ∠TWP is 90°

We can find ∠SWQ from subtracting ∠QWP and ∠SWT from ∠TWP. (90 – 28 – 13 = 49). Thus ∠SWQ = 49°

From the figure, we can see that ∠SWQ and ∠UWV are opposite angles (they are formed by the intersection of two straight lines and share the same vertex)

Opposite angles are always equal to each other and we can say that ∠SWQ  = ∠UWV = 49°

2. In the figure below, VWXY is a rhombus. XYZ is a straight line and ∠VWY = 36°. Find ∠VYZ.

Some of the properties of a rhombus are:

1. All four sides of the rhombus are equal in length
2. Opposite sides of a rhombus are parallel to each other
3. The two opposite pairs of angles within the rhombus are equal to each other

We can say that ∠VWY = ∠XWY = 36°. And thus ∠VWX = ∠VYX = 72° (36° x 2)

Since XYZ is a straight line, ∠VYZ = 180°  – ∠VYX = 180° – 72° = 108°