Question

the quadrilateral shown is a rectangle. label the missing measures. ac = td = ab = m∠atb =

Explanation:

Step1: Recall rectangle properties

In a rectangle, the diagonals are congruent and bisect each other. So \(AC = BD\) and \(AT=TC\), \(BT = TD\). Given \(BT = 15\), then \(TD=15\) and \(AC=BD = 2\times15=30\).

Step2: Find \(AB\)

In right - triangle \(ABC\), we can use the Pythagorean theorem. But also note that opposite sides of a rectangle are equal. Since \(DC = 25\), then \(AB = 25\).

Step3: Find \(\angle ATB\)

\(\angle ATB\) and the given \(110^{\circ}\) angle are vertical angles. Vertical angles are equal, so \(m\angle ATB=110^{\circ}\).

Answer:

\(AC = 30\)
\(TD = 15\)
\(AB = 25\)
\(m\angle ATB=110^{\circ}\)