Advertisements
Advertisements
प्रश्न
The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?
Advertisements
उत्तर
\[\text{ The sides of the quadrilateral ABCD are produced in order (according to figure) . } \]
\[\text{ Now, we need to find the sum of the exterior angles } . \]
\[\text{ Since the angles made on the same side of straight line are } 180 °, \text{ i . e . , linear pair, we have: } \]
\[a + x + b + y + c + z + w + d = 180° + 180° + 180° + 180°= 720° \]
\[OR \]
\[\text{ Sum of the interior angles + sum of exterior the angles } = 180 ° \times 4 = 720° \]
\[ \text{ Since the sum of the interior angles of a quadrilateral is } 360° , \text{ we have } : \]
\[w + x + y + z = 360° \]
\[ \text{ Substituing the value, we get } : \]
\[a + b + c + d = 360° \]
\[ \therefore \text{ Sum of the exterior angles } = 360 ° \]
APPEARS IN
संबंधित प्रश्न
Complete of the following, so as to make a true statement:
A quadrilateral has .... diagonals.
Complete of the following, so as to make a true statement:
A quadrilateral is convex if, for each side, the remaining ______ lie on the same side of the line containing the side.
A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?
In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.
If ABCD is a rectangle with ∠BAC = 32°, find the measure of ∠DBC.
The angles of a pentagon are x°, (x - 10)°, (x + 20)°, (2x - 44)° and (2x - 70)°. Find the angles.
If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠C and ∠D at R and of ∠D and ∠A at S, then PQRS is a ______.
The number of obtuse angles in the following figure is ______.
In the following figure, name any two angles that appear to be obtuse angles.
Using the information given, name the right angles in part of figure:
OP ⊥ AB
