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gmany

Answer:

[tex]\huge\boxed{x=65}[/tex]

Step-by-step explanation:

Look at the picture.

[tex]m\angle VUP=180^o-2\cdot60^o=180^o-120^o=\boxed{60^o}\\\\m\angle UPQ=360^o-2\cdot60^o=360^o-120^o=\boxed{240^o}\\\\m\angle QRM=180^o-2\cdot60^o=180^o-120^o=60^o\\\\m\angle RMQ=180^o-135^o=45^o\\\\in\ \triangle QRM:\ m\angle MQR=180^o-(60^o+45^o)=180^o-105^o=75^o\\\\m\angle PQW=360^o-(2\cdot60^o+75^o+80^o)=360^o-(120^o+155^o)\\\\=360^o-275^o=\boxed{85^o}\\\\m\angle UVW=\boxed{90^o}[/tex]

VWQPU is the pentagon. The sum of interior angles in a pentagon is equal 540°. Therefore:

[tex]x^o=540^o-(90^o+60^o+240^o+85^o)=540^o-475^o=65^o[/tex]

View image gmany
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