Question

∠CAT and ∠MUD are supplementary. If m∠CAT=11x+16 and m∠MUD=4x+14, find the measure of each angle.

Answer 1

Answers:

• x = 10
• angle CAT = 126 degrees
• angle MUD = 54 degrees

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Explanation:

∠CAT and ∠MUD are supplementary, which means the angle measures add to 180. They form a straight line.

( m∠CAT ) + ( m∠MUD ) = 180

( 11x+16 ) + ( 4x+14 ) = 180

11x+16 + 4x+14 = 180

(11x+4x) + (16+14) = 180

15x+30 = 180

15x = 180-30

15x = 150

x = 150/15

x = 10

Let's find each angle based on this x value

• m∠CAT=11x+16 = 11*10+16 = 110+16 = 126 degrees
• m∠MUD=4x+14 = 4*10+14 = 40+14 = 54 degrees

Those two angles add to 126+54 = 180 to confirm we do indeed have supplementary angles, and confirm the correct answers.