Question

The measures of the angles of a quadrilateral in degrees are x, 3x – 40, 2x, 4x + 20. Find the measure of each angle.

Answer 1

Hint: As we know that the sum of the measure of all the three angles of a triangle is 180°.
Similarly, the sum of the measure of all the four angles of a quadrilateral is 360°.
So, in this question, we will sum up all the four measures of the angle of the quadrilateral and equate it to 360°.

Complete step-by-step answer:
As mentioned in the hint above, we will add all the four measures of the angle of the quadrilateral and equate it to 360°, because the sum of all the four angles of a quadrilateral is always 360°.
So, the given measures of the four angles are x; 3x – 40; 2x; 4x +20
Sum of the measure of the angles of a quadrilateral = 360°
(x)° + (3x – 40)° + (2x)° + (4x +20)° = 360°
Solving the equation:-
(x)° + (3x – 40)° + (2x)° + (4x +20)° = 360°
x + 3x – 40 + 2x + 4x + 20 = 360
x + 3x + 2x + 4x – 40 + 20 = 360
4x + 6x – 20 = 360
10x = 360 + 20
x = 38
Now, substituting the value of ‘x’ into all the four measures of the angles:-
(x)° = 38°
(3x – 40)° = 3 x 38 – 40 = 114 – 40 = 74°
(2x)° = 2 x 38 = 76°
(4x +20)° = 4 x 38 + 20 = 152 + 20 = 172°
Verification:-
38° + 74° + 76° + 172° = 360°
360° = 360°
Hence, verified.
Therefore, the values of the measures of the four angles of the quadrilateral are 38°; 74°; 76°; 172°.

Note: One must remember the sum of measures of the angles of different shapes because they can come in handy. Here are the sums of measures of the angles of some basic shapes:-
1) TRIANGLE: The sum of the measure of the angles of a triangle is always 180°.
2) QUADRILATERAL: The sum of the measure of the angles of any quadrilateral is always 360°.
3) PENTAGON: The sum of the measure of the angles of a pentagon is always 540°. The number of sides in a Pentagon is 5.
4) HEXAGON: The sum of the measure of the angles of a hexagon is always 720°. The number of sides in a hexagon is 6.