12. If the three angles of a quadrilateral are 100°, 130°, 60° then what is the fourth angle?
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Answer:
70 degrees
Step-by-step explanation:
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Given :
- Three angles of quadrilateral = 100°, 130°, 60°
To find :
- Measure of fourth angle of the quadrilaterals.
Explanation :
Let the fourth angle of the quadrilateral be ∠x
As we know that,
Measure of all angles of the quadrilateral = 360°
∴ 100° + 130° + 60° + ∠x = 360° [ angle sum property ]
⇒ 290° + ∠x = 360°
⇒ ∠x = 70° ✔️
Hence, the measure of 4th angle is 70°.
Points to keep in mind :-
- A quadrilateral has four sides and four angles.
- The measure of four angles of a quadrilateral is equal to 360°. This property is known as angle sum property of the quadrillion.
- Such type of questions can be solved by applying the angle sum property and then by finding the unknown angle.
- The sum of angles in a triangle is 180°.
- A triangle has three sides and three angles.
- Example of some quadrilateral : square, rectangle, rhombus, parallelogram, trapezium, etc.
- Square is considered as a special quadrilateral that has properties of almost every quadrilateral.
Properties of a square :-
- All the sides are of equal length.
- All angles have the same measure.
- Diagonals have the same length and they bisect each other at 90°.
- All angles are right angle.
Properties of Rhombus :-
- It is also considered as a Diamond. ( because of it's diamond shape. )
- Opposite angles have equal measure.
- Diagonals bisects these equal angles.
- Opposite sides are parallel to each other in a rhombus.
- Diagonals bisect each other at 90°.
- The adjacent angles have the sum equal to 180°.
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