Advertisements
Advertisements
Question
PQRSTU is a regular hexagon. Determine each angle of ΔPQT.
Advertisements
Solution
\[\text{ A regular hexagon is made up of 6 equilateral triangles } . \]
\[So, ∠PQT = 60° \text{ and } ∠QTP = 30° \]
\[\text{ Since the sum of the angles of ∆ PQT is } 180° , \text{ we have } : \]
\[ ∠P + ∠Q + ∠T = 180\]
\[ \Rightarrow ∠P + 60° + 30°= 180° \]
\[ \Rightarrow ∠P = 180° - 90° \]
\[ \Rightarrow ∠QPT = 90° \]
\[ \therefore \text{ The angles of the triangle are 90° , 60° and } 30° .\]
APPEARS IN
RELATED QUESTIONS
Given here are some figures:
 |
 |
 |
 |
 |
 |
 |
 |
Classify each of them on the basis of the following:
- Simple curve
- Simple closed curve
- Polygon
- Convex polygon
- Concave polygon
The perimeter of a parallelogram is 22 cm . If the longer side measures 6.5 cm what is the measure of the shorter side?
A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?
Complete the following statement by means of one of those given in brackets against each:
If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ...............
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120. find angles B and D.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.
A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is ______.
The diagonals of the quadrilateral DEFG are ______ and ______.
An angle is said to be trisected, if it is divided into three equal parts. If in the following figure, ∠BAC = ∠CAD = ∠DAE, how many trisectors are there for ∠BAE?
