A quadrilateral can be formed when the sum of the four given angle measures is equal to 360^(∘).
Practice makes perfect
We want to determine whether we can draw a quadrilateral with angle measures of 60^(∘), 60^(∘), 120^(∘), and 120^(∘). We can recall that a quadrilateral can be formed when the sum of the angle measures is equal to 360^(∘). Let's check whether the four angle measures add up to 360^(∘).
60^(∘) + 60^(∘) + 120^(∘)+ 120^(∘) = 360^(∘) ✓
The sum of the angle measures is 360^(∘). Now we can construct our quadrilateral. We can begin by drawing a segment of any length, and measuring the angles 60^(∘) and 60^(∘) with a protractor. We can denote the angle measures as m∠ A= 60 and m∠ B= 60.
The next step is to set a point on the ray starting at B. We can denote the third vertex as point C. Let's use a protractor to measure m∠ C= 120.
Finally, vertex D is the point of intersection of the rays starting at A and C. We can use the protractor to confirm that the measure of the remaining angle is 120^(∘). We can do so in two steps.
Place the center line of the protractor on top of DA.
Measure the angle between CD and DA.
Let's do it!
The angle formed at D has a measure of 120^(∘). In this case, we can draw a quadrilateral with the given measures.
