Grade 7 - Mathematics 8.3 Problems on Quadrilaterals - II
Example:
In a quadrilateral, two angles are 80° and 120°, the remaining two angles are equal. What is the measure of each of these angles?
Solution:
Sum of the given angles = 80 + 120 = 200.
we know that the sum of the four angles of the quadrilateral is 360°.
\ The sum of the remaining two angles = 360 - 200 = 160
But they are equal.
\ each angle = 1/2 * 160 = 80°.
Example:
In a quadrilateral, the second angle is 2 times the first. The remaining 2 angles are equal and each angle is 4 times the first angle. What is the measure of each of these angles?
Solution:
Let the first angle be 'x'.
We know that the sum of the angles of a quadrilateral = 360°.
Here, Second angle = 2x; Third angle = Fourth angle = 4x;
Therefore x + 2x + 4x + 4x = 360;
ie 11x = 360;
ie x = 360/11 = 32.73.(Rounded off to nearest hundredth).
Hence the first angle is 32.73°,
second angle = 2 x 32.73 = 65.46° and third angle = Fourth angle = 4 x 32.73 = 130.92°.
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 equal and are 5 times the first. What is the measure of each of these angles?
In a quadrilateral, two angles are 80° and 100°, the remaining two angles are equal. What is the measure of each of these angles?
