Question

1. Two angles of a quadrilateral measure 140° and 80°. T1. The other two angles are in a ratio of 3:4. What is the value of x? What are the measures of those two angles? x =

2.Next, list the measures of the other two angles from lowest to highest.

Answer 1

Angles are 3x, 4x =
`60\°,80\°`

Angles from lowest to highest:
`60\°,60\°,80\°,140\°`

Explanation:

Given: Two angles of a quadrilateral measure 140° and 80°. The other two angles are in a ratio of 3:4.

To find: value of x, measures of those two angles and

Also, to list the measures of the other two angles from lowest to highest.

Solution:

According to angle sum property of a quadrilateral, sum of angles of a quadrilateral is 180°.

Let the two angles be 3x and 4x

`3x+4x+140\°+80\°=360\°\\7x+220\°=360\°\\7x=360\°-220\°=140\°\\x=(140\°)/(7)=20\°\\`

So, angles are as follows:

`3x=3(20\°)=60\°\\4x=4(20\°)=80\°`

Angles from lowest to highest:
`60\°,60\°,80\°,140\°`