Quadrilateral and angles

In a quadrilateral, angle α is twice as large as angle β. Angle γ is 80% of angle α, and angle δ is 30° greater than angle α. Determine the angles of this quadrilateral.

Correct answer:

α =  68.75 °
β =  137.5 °
γ =  55 °
δ =  98.75 °

Step-by-step explanation:

r=80%=10080​=54​=0.8 α+β+γ+(30+α)=360 β=2⋅ α γ=r⋅ α  α+2⋅ α+r⋅ α+(30+α)=360 α+2⋅ α+0.8⋅ α+(30+α)=360  4.8α=330  α=4.8330​=68.75  α=4275​=68.75=68.75∘=68°45′
β=2⋅ α=2⋅ 68.75=137.5∘=137°30′
γ=r⋅ α=0.8⋅ 68.75=55∘
δ=30+α=30+68.75=98.75∘=98°45′

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Our percentage calculator will help you quickly and easily solve a variety of common percentage-related problems.
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: