We are given that the ratio of the measures of the angles of the quadrilateral is 6:5:4:3. We can rewrite this extended ratio by adding x to each number.
6:5:4:3 ⇒ 6 x:5 x:4 x:3 x
Now, let's recall that the sum of the angle measures in a quadrilateral is always equal to 360^(∘). Using this information, we can write an equation.
6 x+5 x+4 x+3 x= 360
We will solve this equation to find the value of x.
The value of x is 20. By substituting this number into our extended ratio, we will find all angle measures of this quadrilateral.
6 x:5 x:4 x:3 x
⇓
6( 20):5( 20):4( 20):3( 20)
⇓
120:100:80:60
This quadrilateral has angle measures of 120^(∘),100^(∘),80^(∘) and 60^(∘). As we can see, 140^(∘) is not an angle measure of this figure. Therefore, answer D is correct.
