Question

problem:
the angles of a quadrilateral are ( x ), ( 5x + 15^circ ), ( 3x - 25^circ ), and ( 4x - 20^circ ). find the measure of the largest angle of the quadrilateral in degrees.
(based on section 8.1 of the textbook)
your answer \135\ is incorrect. please try again.
your response(s):
135

Explanation:

Step1: Recall quadrilateral angle sum

The sum of the interior angles of a quadrilateral is \(360^\circ\). So we set up the equation: \(x + (5x + 15^\circ) + (3x - 25^\circ) + (4x - 20^\circ) = 360^\circ\).

Step2: Simplify the left - hand side

Combine like terms: \(x+5x + 3x+4x+15^\circ- 25^\circ - 20^\circ=360^\circ\).
\(13x-30^\circ = 360^\circ\).

Step3: Solve for \(x\)

Add \(30^\circ\) to both sides: \(13x=360^\circ + 30^\circ=390^\circ\).
Divide both sides by 13: \(x=\frac{390^\circ}{13} = 30^\circ\).

Step4: Find each angle

• For \(x\): \(x = 30^\circ\)
• For \(5x + 15^\circ\): \(5\times30^\circ+15^\circ=150^\circ + 15^\circ=165^\circ\)
• For \(3x - 25^\circ\): \(3\times30^\circ-25^\circ = 90^\circ-25^\circ = 65^\circ\)
• For \(4x - 20^\circ\): \(4\times30^\circ-20^\circ=120^\circ - 20^\circ = 100^\circ\)

Answer:

The measure of the largest angle is \(165^\circ\)