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
PQRSTU is a regular hexagon. Determine each angle of ΔPQT.
Complete the following statement by means of one of those given in brackets against each:
If one pair of opposite sides are equal and parallel, then the figure is ........................
If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that ∠C + ∠D = k ∠AOB, then find the value of k.
Mark the correct alternative in each of the following:
The opposite sides of a quadrilateral have
The consecutive sides of a quadrilateral have
Use the following figure to find the value of x
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
The angles of a hexagon are (2x + 5)°, (3x - 5)°, (x + 40)°, (2x + 20)°, (2x + 25)° and (2x + 35)°. Find the value of x.
ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is ______.
How many diagonals does a quadrilateral have?
