Two adjacent angles of a parallelogram are (3x-4)° and (3x+16)°. Find the value of x and hence find the measure of the two angles.

Given:

Two adjacent angles of a parallelogram are $(3x-4)^o$ and $(3x+16)^o$.

To do:

We have to find the value of $x$ and measure of the two angles. 

Solution: 

We know that,

Sum of the angles in a parallelogram is $360^o$ and opposite angles of a parallelogram are equal.

Therefore,

The four angles of the parallelogram are $(3x-4)^o, (3x+16)^o, (3x-4)^o$ and $(3x+16)^o$.

$(3x-4)^o+(3x+16)^o+(3x-4)^o+(3x+16)^o=360^o$

$12x+(-4+16-4+16)^o=360^o$

$12x=(360-24)^o$

$x=\frac{336^o}{12}$

$x=28^o$

$\Rightarrow (3x-4)^o=[3(28)-4]^o=80^o$

$\Rightarrow (3x+16)^o=[3(28)+16]^o=100^o$

The measure of the two angles of the parallelogram is $80^o$ and $100^o$.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

26 Views

Kickstart Your Career

Get certified by completing the course

Get Started