Question

the following diagram shows a parallelogram.
find the measures of the following

( y = )
( m angle t r k = ) degrees

Explanation:

Step1: Use the property of parallelogram (alternate - interior angles)

In a parallelogram \(TRAC\), \(TA\parallel CR\). So, \(\angle TCR=\angle TRK\) (alternate - interior angles). That is \(y + 17=2y-5\).

Step2: Solve the equation for \(y\)

Subtract \(y\) from both sides of the equation \(y + 17=2y-5\):
\(y+17 - y=2y - 5-y\)
\(17=y - 5\)
Add \(5\) to both sides: \(y=17 + 5=22\)

Step3: Find \(m\angle TRK\)

Substitute \(y = 22\) into \(y + 17\) (or \(2y-5\)).
\(m\angle TRK=y + 17\)
\(m\angle TRK=22+17=39\)

Answer:

\(y = 22\), \(m\angle TRK=39\) degrees