Chapter 6, Problem 11CR

Solution

a.

The measurement of $\angle F$

The measurement of $\angle F$ is ${140}^{\circ }$

Given: FGHJ is a quadrilateral, $FG=x+5$ , $GH=2x+3$ , $\angle G={40}^{\circ }$ and $\angle J={(4x+12)}^{\circ }$

Concept used: Formula of perimeter has been used here which is

Perimeter of quadrilateral = Sum of all sides

And, angle sum property has also been used in this question.

Calculation: Here, In quadrilateral $\angle F+\angle G+\angle H+\angle J={360}^{\circ }$ (angle sum property)

  $\angle F+{40}^{\circ }+\angle H+(4x+{12}^{\circ })={360}^{\circ }$

  $\angle F+\angle H+4x^{\circ }$ = ${360}^{\circ }-{52}^{\circ }$ = ${308}^{\circ }$

And, $2\angle F+2\angle G={360}^{\circ }$

➔ $2\angle F+{80}^{\circ }={360}^{\circ }$

➔ $2\angle F={280}^{\circ }$

➔ $\angle F={140}^{\circ }$

Conclusion: Hence, the measurement of $\angle F$ is ${140}^{\circ }$

b.

The perimeter of FGHJ

The perimeter of FGHJ is $58$

Given: FGHJ is a quadrilateral, $FG=x+5$ , $GH=2x+3$ , $\angle G={40}^{\circ }$ and $\angle J={(4x+12)}^{\circ }$

Concept used: Formula of perimeter has been used here which is

Perimeter of quadrilateral = Sum of all sides

And, angle sum property has also been used in this question.

Calculation: Here, perimeter of FGHJ = $2FG+2GH$

➔ $2(7+5)+2(14+3)$

➔ $24+34$

➔ $58$

Conclusion: Hence, the perimeter of FGHJ is $58$