Question

17.
(2y + 2)°
120°
20
20°
120

Explanation:

Step1: Sum of interior angles of quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\).

Step2: Calculate the sum of known angles

The sum of angles at \(T\) is \(20^{\circ}+20^{\circ} = 40^{\circ}\), and the sum of angles at \(R\) and \(V\) is \(120^{\circ}+120^{\circ}=240^{\circ}\).

Step3: Set up equation for angle at \(W\)

Let the angle at \(W\) be \((2y + 2)^{\circ}\). Then \((2y+2)+40 + 240=360\).
Simplify the left - hand side: \(2y+2+280 = 360\), so \(2y+282=360\).
Subtract \(282\) from both sides: \(2y=360 - 282\), \(2y = 78\).
Divide both sides by \(2\): \(y=\frac{78}{2}=39\).

Answer:

\(y = 39\)