Advertisements
Advertisements
Question
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
Advertisements
Solution
\[\text{ Since the sum of all the angles of a hexagon is } 720° , \text{ we get } : \]
\[x° + \left( x - 5 \right)° + \left( x - 5 \right)° + \left( 2x - 5 \right)° + \left( 2x - 5 \right)° + \left( 2x + 20 \right)° = 720°\]
\[ \Rightarrow x° + x° - 5° + x°- 5°+ 2x - 5°+ 2x - 5°+ 2x + 20°= 720° \]
\[ \Rightarrow 9x - 20° + 20° = 720° \]
\[ \Rightarrow 9x = 720° \]
\[ \therefore x = 80\]
RELATED QUESTIONS
How many diagonals does following have?
A regular hexagon
ABCD is a parallelogram, AD is produced to E so that DE = DC and EC produced meets AB produced in F. Prove that BF = BC.
In a quadrilateral, define of the following Opposite angles .
Complete the following statement by means of one of those given in brackets against each:
If opposite angles of a quadrilateral are equal, then it is necessarily a ....................
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ∠QRS = 100°, then ∠TVS =
If one angle of a cyclic quadrilateral is 75°, then the opposite angle is
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 ______.
Using the information given, name the right angles in part of figure:
AC ⊥ BD
Using the information given, name the right angles in part of figure:
AE ⊥ CE
