Question

the adjacent figure HOPE,is a parallelogram. find the angle measure of x,y and z.state the properties you used to find them.​

Answer 1

step by step explanation

Since HOPE is a parallelogram, therefore, HE∥OP and 

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EP

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30o

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)⇒y=40o

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)⇒y=40oSince opposite angles are equal in a parallelogram.

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)⇒y=40oSince opposite angles are equal in a parallelogram.∴∠HEP=∠HOP

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)⇒y=40oSince opposite angles are equal in a parallelogram.∴∠HEP=∠HOP⇒x=180o−∠POX=180o−70o=110o

Since HOPE is a parallelogram, therefore, HE∥OP and HO∥EPNow, HE∥OP and transversal HO intersects them.∴∠EHO=∠POX[∵ Corresponding angles are equal]∠40o+z=70o⇒z=70o−40o=30oAgain, HE∥OP and transversal HP intersects them.∴∠OPH=∠EHP[∵ Alternate angles are equal)⇒y=40oSince opposite angles are equal in a parallelogram.∴∠HEP=∠HOP⇒x=180o−∠POX=180o−70o=110oHence, x=110o,y=40o and z=30o

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