Quadrilateral Angles Ratio Calculation
The sum of the interior angles of any quadrilateral is always 360 degrees. We are given that the angles are in the ratio 2 : 4 : 6 : 8.
Representing Quadrilateral Angles
- Let the angles be represented as $2x$, $4x$, $6x$, and $8x$, where $x$ is a common factor.
Calculating the Angles
We set up an equation using the sum of the angles:
$2x + 4x + 6x + 8x = 360^\circ$
Combine the terms:
$20x = 360^\circ$
Solve for $x$:
$x = \frac{360^\circ}{20}$
$x = 18^\circ$
Finding the Smallest Angle
Now, we find the measure of each angle:
- Angle 1: $2x = 2 \times 18^\circ = 36^\circ$
- Angle 2: $4x = 4 \times 18^\circ = 72^\circ$
- Angle 3: $6x = 6 \times 18^\circ = 108^\circ$
- Angle 4: $8x = 8 \times 18^\circ = 144^\circ$
The smallest angle corresponds to the smallest part of the ratio, which is $2x$. Therefore, the smallest angle is $36^\circ$.
Similar Questions
- If one angle of a parallelogram is $18^\circ$ less than twice the smallest angle of the same parallelogram, then the largest angle of the parallelogram is:
- Find the area of a trapezium whose parallel sides are 10 cm and 20 cm and non-parallel sides are equal to 10 cm.
- The angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7. What is the difference between the largest and the smallest angle?
- If ABCD is a cyclic quadrilateral and ABC is an equilateral triangle find the angle of CDA.
- If one angle of a parallelogram is $39^\circ$ less than twice the smallest angle, then the smallest angle of the parallelogram is:
- If one angle of a parallelogram is $30^\circ$ less than twice the measure of the smallest angle, then the measure of the largest angle of the parallelogram is:
- In a rhombus ABCD, if $\angle ACB = 40^\circ, \text{then } \angle ADB = ?$
- P is the mid-point of side BC of a parallelogram ABCD such that $\angle BAP = \angle DAP$.
If AD = 10 cm, then CD = ? - If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12, then the largest of these angles is:
- The diagonals of a quadrilateral ABCD bisect each other. In this quadrilateral, if $\angle A = 45^{\circ}$ then $\angle B =$ ?
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
