Question

the diagram shows a convex polygon. diagram with angles: ( 4u - 32^circ ), ( u ), ( 5u - 50^circ ), ( 2u - 38^circ ) what is the value of ( u )? ( u = square^circ )

Explanation:

Step1: Recall the exterior angle sum of a convex polygon.

The sum of the exterior angles of any convex polygon is \( 360^\circ \). So we can set up the equation: \( (4u - 32)^\circ+(u)^\circ+(2u - 38)^\circ+(5u - 50)^\circ = 360^\circ \).

Step2: Combine like terms.

First, expand the left - hand side: \( 4u-32 + u+2u - 38+5u - 50=360 \).
Combine the \( u \) terms: \( (4u + u+2u + 5u)+(-32-38 - 50)=360 \).
\( 12u-120 = 360 \).

Step3: Solve for \( u \).

Add 120 to both sides of the equation: \( 12u-120 + 120=360 + 120 \).
\( 12u=480 \).
Divide both sides by 12: \( u=\frac{480}{12}=40 \).

Answer:

\( 40 \)