If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure o

If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?

If the angles of a quadrilateral are in the ratio 1:2:3:4, what is the measure of the largest angle?

Step 1: Understand that a quadrilateral has four angles.
Step 2: Let the angles be represented as x, 2x, 3x, and 4x based on the given ratio of 1:2:3:4.
Step 3: Write down the equation for the sum of the angles in a quadrilateral: x + 2x + 3x + 4x = 360 degrees.
Step 4: Combine the terms on the left side: 1x + 2x + 3x + 4x = 10x.
Step 5: Set up the equation: 10x = 360 degrees.
Step 6: Solve for x by dividing both sides by 10: x = 36 degrees.
Step 7: Find the largest angle by calculating 4x: 4 * 36 = 144 degrees.
Step 8: Conclude that the measure of the largest angle is 144 degrees.

Angle Sum Property of Quadrilaterals – The sum of the interior angles of a quadrilateral is always 360 degrees.
Ratios – Understanding how to express quantities in terms of ratios and solve for unknowns.
Algebraic Manipulation – Using algebra to solve equations derived from geometric properties.