Trapezoid and Quadrilateral Problems, 7

Category: Plane Geometry

"Published in Newark, California, USA"

Two congruent angles of an isosceles trapezoid have measures 3x + 10 and 5x - 10. Find the value of x and then give the measures of all angles of the trapezoid.

Solution:

To illustrate the problem, it is better to draw the figure as follows 

Photo by Math Principles in Everyday Life

Isosceles trapezoid is a trapezoid whose two opposite sides and two adjacent angles are congruent. If the two adjacent angles of the lower base are congruent, then the two adjacent angles of the upper base are also congruent.
 
For any trapezoid, the two adjacent sides of a leg are supplementary angles because the upper and lower bases are parallel. 

If that's the case, the value of x is

 

 

Hence, the measurement of an angle at the lower base of an isosceles trapezoid is
 

 

 

and at the upper base is
 

 

 

Therefore, the measurements of the two congruent angles of an isosceles trapezoid are 77.5° and 102.5°.
 

Trapezoid and Quadrilateral Problems, 6

Category: Plane Geometry

"Published in Newark, California, USA"

One angle of an isosceles trapezoid has measure 57°. Find the measures of the other angles.

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Isosceles trapezoid is a trapezoid whose two opposite sides and two adjacent angles are congruent. If the two adjacent angles of the lower base are congruent, then the two adjacent angles of the upper base are also congruent.
 
For any trapezoid, the two adjacent sides of a leg are supplementary angles because the upper and lower bases are parallel. 
 
Therefore, the other angles of an isosceles trapezoid are
 

 

 

 
There's another way in solving for the other angles of an isosceles trapezoid. For any four closed figures like quadrilateral, trapezoid, parallelogram, rhombus, rectangle, and square, the sum of their internal angles is equal to 360°. 
 
Therefore, the other angles of an isosceles trapezoid are
 

 

 

 

 

Trapezoid and Quadrilateral Problems, 5

Category: Plane Geometry

"Published in Newark, California, USA"

Given a trapezoid with its median. Find the value of x.

Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above 

Photo by Math Principles in Everyday Life

If a theorem says "The median of a trapezoid is parallel to the bases and has a length equal to the average of the base lengths.", then the value of x, therefore is