In a quadrilateral ABCD, if m \ B \= 40 m \< C \= 2x m \< D \= 40, then m \< C is equal to:

ESIC Nursing Officer -2019 (Shift -1)

Non Nursing Subjects

Medium

In a quadrilateral ABCD, if m < A = 2x m > B = 40 m < C = 2x m < D = 40, then m < C is equal to:

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

The fundamental property of any quadrilateral is that the sum of its four interior angles is always 360°.
An equation is formed by summing the given angles: 2x + 40° + 2x + 40° = 360°.
Solving the equation (4x + 80° = 360°) yields x = 70°.
The measure of angle C is given by the expression 2x.
Substituting the value of x, m∠C = 2 * 70°, which equals 140°.

Option B: If m∠C were 100°, then 2x = 100, meaning x = 50°. The sum of the angles would be 2(50) + 40 + 2(50) + 40 = 100 + 40 + 100 + 40 = 280°, which is not equal to 360°. This is a calculation error.
Option C: If m∠C were 160°, then 2x = 160, meaning x = 80°. The sum of the angles would be 2(80) + 40 + 2(80) + 40 = 160 + 40 + 160 + 40 = 400°, which is not equal to 360°. This is a calculation error.
Option D: If m∠C were 120°, then 2x = 120, meaning x = 60°. The sum of the angles would be 2(60) + 40 + 2(60) + 40 = 120 + 40 + 120 + 40 = 320°, which is not equal to 360°. This is a calculation error.

Visual 1: Diagram - An illustration of a general quadrilateral labeled ABCD, with each angle marked with its corresponding expression (m∠A=2x, m∠B=40°, m∠C=2x, m∠D=40°). This helps visualize the problem setup.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Properties of Quadrilaterals as background academic context rather than a clinical decision trigger.
This question tests basic geometry and algebraic skills, which are part of the general intelligence and numerical ability sections of many competitive examinations, including those for nursing.
Strong analytical and problem-solving skills are essential for nurses to interpret data, calculate dosages, and make critical decisions.
What if the shape was a pentagon? The sum of interior angles would be (5-2) × 180° = 540°, and the equation would be set to equal 540 instead of 360.

How to Approach the Question

Identify the geometric shape mentioned in the question, which is a quadrilateral.
Recall the fundamental property of this shape: the sum of the interior angles of a quadrilateral is 360°.
Write down the given values for each of the four angles.
Set up an algebraic equation by adding all the angle expressions and equating the sum to 360.
Solve the equation to find the value of the variable 'x'.
Substitute the value of 'x' back into the expression for the required angle (m∠C = 2x) to find the final answer.

Concept Tested & Keywords

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