Question

If m ∠ F D E = ( 3 x − 15 ) ° and m ∠ F D B = ( 5 x + 59 ) ° , find the value of x such that ∠ F D E and ∠ F D B are supplementary.

Answer 1

• x = 17

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Supplementary angles sum to 180°.

Given

• m∠FDE = (3x - 15)° and m∠FDB = (5x + 59)°,
• ∠FDE and ∠FDB are supplementary

Set equation and solve for x

• 3x - 15 + 5x + 59 = 180
• 8x + 44 = 180
• 8x = 180 - 44
• 8x = 136
• x = 136/8
• x = 17