The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°.
How to determine a missing angle within a geometrical system
By Euclidean geometry we know that squares are quadrilaterals with four sides of equal length and four right angles and triangles are equilateral when its three sides have equal length and three angles with a measure of 60°. In addition, a complete revolution has a measure of 360°.
Finally, we must solve the following equation for the angle QUP:
m∠QUR + m∠QUP + m∠PUT + m∠RUT = 360
60 + m∠QUP + 60 + 90 = 360
m∠QUP + 210 = 360
m∠QUP = 150
The size of the angle QUP in the system formed by the equilateral triangle QUR, the equilateral triangle PUT and the square RUTS is equal to 150°. [tex]\blacksquare[/tex]
To learn more on quadrilaterals, we kindly invite to check this verified question: https://brainly.com/question/13805601
