Question

what is the value of t?
w
56°
100°
x
t=
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Use the property of congruent triangles (SSS)

Since \( WX = VU\), \( WV = XU\), and \( WU\) is common, \(\triangle WXU\cong\triangle VUW\) (by S - S - S congruence criterion). So, \(\angle XWU=\angle VUW\) and \(\angle WXU=\angle UVW\).

Step2: Use the angle - sum property of a quadrilateral

The sum of interior angles of a quadrilateral \(WXUV\) is \((4 - 2)\times180^{\circ}=360^{\circ}\). Let \(\angle XWU = 56^{\circ}\), \(\angle V = 100^{\circ}\), and \(\angle WXU=t\).
We know that \(\angle XWU+\angle V+\angle WXU+\angle VUW = 360^{\circ}\). But \(\angle XWU=\angle VUW = 56^{\circ}\).
Substitute the values into the formula: \(56^{\circ}+100^{\circ}+t + 56^{\circ}=360^{\circ}\).
Simplify the left - hand side: \(212^{\circ}+t=360^{\circ}\).

Step3: Solve for \(t\)

Subtract \(212^{\circ}\) from both sides of the equation: \(t=360^{\circ}-212^{\circ}\).

Answer:

\(t = 56^{\circ}\)