because that reference:In figure ABCD is a parallelogram and also the triangle APB, AQD and also CRD are equilateral. Uncover x. (answer: $120^circ$)

*

My progress:I found the complying with links and also put it in the drawing$AF = FC\BF = FD\measuredangle QEG = 60^o\measuredangle DAC = measuredangle ACB$

but ns can"t finish..

You are watching: Find the measure of angle x in the figure below:

*


*

Please keep in mind that $angle PAQ = angle BAD$, $AP = AB$, $AQ = AD$.

So $ riangle PAQ cong riangle poor $ and also hence $angle AQP = angle ADB$

Similarly show that $ riangle RDQ cong riangle CDA$ and also so, $angle DQR = angle CAD$

But $angle ADB + angle CAD = 180^circ - x $ (see $ riangle AOD$ whereby $O$ is the allude of intersection that diagonals in the parallel $ABCD$)

That leader to,

$angle PQR = x = 180^circ - x + 60^circ implies x = 120^circ$


*

Thanks for contributing an answer to 4476mountvernon.com Stack Exchange!

Please be sure to answer the question. Administer details and also share her research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based upon opinion; earlier them up with referrals or personal experience.

Use 4476mountvernon.comJax to style equations. 4476mountvernon.comJax reference.

See more: Madonna Exposes Fans Breast Uncensored, Madonna Exposes Fan'S Breast During Concert

To find out more, watch our tips on writing good answers.


write-up Your prize Discard

By clicking “Post her Answer”, girlfriend agree come our terms of service, privacy policy and also cookie plan


Not the price you're spring for? Browse various other questions tagged geometry or questioning your very own question.


*

site style / logo © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.19.40496


4476mountvernon.comematics stack Exchange works finest with JavaScript permitted
*

your privacy

By clicking “Accept every cookies”, you agree ridge Exchange can store cookies on your machine and disclose info in accordance through our Cookie Policy.