The size of angles of a quadrilateral are x,x+10,x+20,x+30. What is the size of each angle?

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samhouston's profile pic

samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted on

x,x+10,x+20,x+30

The sum of the angles of a quadrilateral is equal to 360 degrees.

x + x + 10 + x + 20 + x + 30 = 360

Combine like terms and solve.

4x + 60 = 360

4x = 300

x = 75

The measurement of the angles are:

x = 75 degrees

x + 10 = 85 degrees

x + 20 = 95 degrees

x + 30 = 105 degrees

You can check this by adding your 4 angle measurements.

75 + 85 + 95 + 105 = 360

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The sum of the angles of a quadrilateral which has four angles is equal to 360 degrees.

This gives x + x + 10 + x + 20 + x + 30 = 360

=> 4x + 60 = 360

=> 4x = 300

=> x = 75 degrees

The angles are 75, 85, 95, 105 degrees.

The angles of the quadrilateral are 75, 85, 95, 105 degrees.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We know that the sum of the interior angles in a polygon with n sides is 180*(n-2).

The number of sides in a quadrilateral is n = 4, therefore the sum of the interior angles is 180*(4-2) = 180*2 = 360 degrees

Therefore, we'll add the given measures of angles:

x + x + 10 + x + 20 + x + 30 = 360

4x + 60 = 360

4x = 360 - 60

4x = 300

x = 75 degrees

x + 10 = 75 + 10 = 85 degrees

x + 20 = 75 + 20 = 95 degrees

x + 30 = 75 + 30 = 105 degrees

The interior angles of the quadrilateral are: 75 ; 85 ; 95 ; 105 degrees.

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