In the given figure, PQRS is a parallelogram in which a pair of opposite angles is given. The value of x is 30, 25, 10, or 15? If the diagonals of a quadrilateral bisect each other... In the given figure, PQRS is a parallelogram in which a pair of opposite angles is given. The value of x is 30, 25, 10, or 15? If the diagonals of a quadrilateral bisect each other at right angles, then the quadrilateral is a trapezium, rhombus, parallelogram, or rectangle? Find x and y given a cyclic quadrilateral ABCD. O is the centre of the circle, find the value of x in given figure. If the semi-perimeter of an equilateral triangle is 12√3 cm, then area of the triangle is 48√3 cm², 16√2 cm², 32√3 cm², or other options? The area of the base of the cone is 154 cm². Its slant height is 15 cm. Curved surface area of the cone is? The volume and surface area of a sphere are numerically equal, then its radius is 2 units, 3 units, 4 units, or other options? The range of the data 25.7, 16.3, 21.8, 21.7, 24.3, 22.7, 24.9 is? What is the final value?
Understand the Problem
The image contains mathematical problems related to geometry and areas of shapes, requiring calculations to find specific values such as angles, areas, and volumes. The problems involve the properties of parallelograms, cyclic quadrilaterals, triangles, cones, and spheres.
Answer
The value of $x$ is $15$.
Answer for screen readers
The value of $x$ is $15$.
Steps to Solve
-
Identify the Angles of the Parallelogram In a parallelogram, opposite angles are equal and consecutive angles are supplementary. You have two angles: $2x + 27^\circ$ and $4x - 3^\circ$.
-
Set Up the Equation Since opposite angles are equal, set the angles equal to each other: [ 2x + 27 = 4x - 3 ]
-
Rearrange the Equation To solve for $x$, first rearrange the equation: [ 2x + 27 + 3 = 4x ] Simplifying gives: [ 30 = 4x - 2x \Rightarrow 30 = 2x ]
-
Solve for x Divide both sides by 2: [ x = \frac{30}{2} = 15 ]
The value of $x$ is $15$.
More Information
In a parallelogram, the properties of opposite and consecutive angles are crucial for calculations. This problem emphasizes understanding the properties of geometric figures.
Tips
- Forgetting that opposite angles in a parallelogram are equal.
- Miscalculating the arithmetic when rearranging the equations.
AI-generated content may contain errors. Please verify critical information
