- Example:
The angles of a quadrilateral are x, x-10, x+30 and 2x. Find the angles.
Solution:
We know that the sum of the four angles of any quadrilateral is 360°.
So, x + (x-10) + (x+30) + 2x = 360
x + x - 10 + x + 30 + 2x = 360
5x + 20 = 360
5x = 360 - 20
5x = 340
x = 340/5
x = 68°
Substituting x value, we get
68°, 58°, 98° and 136°.
- Example:
In a quadrilateral, the first angle is 7 more than the second, 3 less than the third and 5 times the fourth. Find the angles?
Solution:
Let the first angle be 'x'. Then the second angle will be 'x + 7'.
The third angle and fourth angle will be 'x - 3' and '5x' respectively.
Since the sum of the angles of a quadrilateral is 360°;
we have x + x + 7 + x - 3 + 5x = 360;
ie 8x + 4 = 360;
ie 8x = 360 - 4 = 296;
ie x = 296/8 = 37.
Therefore first angle = 37°, second angle = 44°, third angle = 34° and fourth angle = 185° .
Directions: Read the above example carefully and answer the following questions:
- In a quadrilateral, the first angle is 2 times the second, the remaining two angles are 5 more than the first. What is the measure of each of these angles?
- In a quadrilateral, the first angle is 6 times the second, 9 more than the third and 5 less than the fourth. What is the measure of each of these angles?
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