Chapter 11, Problem 6PT

To determine

To find the value of ‘x’ and the missing angles.

Answer to Problem 6PT

  $x=34°$ , Missing angles: $90°$ and $68°$

Explanation of Solution

Given information:

The quadrilateral has angles measuring $80°,122°,\left(x+56\right)°\&2x°$ .

Formula used:

Sum of interior angles in a quadrilateral is $=360°$

Calculation:

Since the sum of interior angles in a quadrilateral is $=360°$ , add the interior angles and solve for ‘x’.

Once the value of ‘x’ is calculated, the remaining interior angles shall be found out.

  $80°+122°+\left(x+56\right)°+2x°=360°$

Equating the interior angles with $360°$

  $=>3x+258°=360°$

Adding the like terms.

  $=>3x=360°-258°$

Taking the numerical terms on the right-hand side.

  $=>3x=102°$

Simplifying the terms.

  $=>x=\frac{102°}{3}$

Getting the value of ‘x’.

  $x=34°$

Since the value is found, next putting this value in the expression signifying the angles with missing values.

  $\left(x+56\right)°=\left(34+56\right)°$

Putting the value of ‘x’.

  $=90°$

Final measure

  $2x°=2\times 34°$

On simplifying,

  $=68°$