Chapter 5.5, Problem 6PSA

Solution

To Calculate: The measure of $\angle D$ and $\angle C$

The measure of $\angle D$ and $\angle C$ are ${134}^{\circ }$ and ${46}^{\circ }$

Given information:

ABCD is a parallelogram.

  $m\angle A=x^{\circ }$

  $m\angle D={\left(3x-4\right)}^{\circ }$

Formula used:

Here, we are using the parallelogram property i.e.,

Consecutive angles of a parallelogram are supplementary

Calculation:

Here, $\angle A+\angle D={180}^{\circ }$

(Consecutive angles of a parallelogram are supplementary)

  $x+3x-4={180}^{\circ }$

  $4x-4={180}^{\circ }$

  $x={46}^{\circ }$

So, $m\angle A={46}^{\circ }$

  $m\angle D={\left(3x-4\right)}^{\circ }$

Putting the value of x

➜ $3\times 46-4$

So, $m\angle D={134}^{\circ }$

And, $\angle C+\angle D={180}^{\circ }$

(Consecutive angles of a parallelogram are supplementary)

  $\angle C+{134}^{\circ }={180}^{\circ }$

  $\angle C={46}^{\circ }$

Conclusion: Hence, the measure of $\angle D$ and $\angle C$ are ${134}^{\circ }$ and ${46}^{\circ }$