Questions: Congruent, Supplementary or Complimentary?

Transcript text: Congruent, Supplementary or Complimentary?

Solution

Solution Steps

Step 1: Set up the equation

Angles $\angle{ABC}$ and $\angle{ABD}$ are supplementary angles. Therefore, their sum is equal to 180°. So, the equation is $(16x+4)^{\circ} + 18x^{\circ}= 180^{\circ}$.

Step 2: Solve for x

Combine like terms: $34x + 4 = 180$. Subtract 4 from both sides: $34x = 176$. Divide both sides by 34: $x = \frac{176}{34} = \frac{88}{17}$. The simplified fraction value is x = 5.176, if a fraction is needed it is $\frac{88}{17}$.

Step 3: Determine the type of angles

Substitute the value of x found in the previous step, $\frac{88}{17}$, back into the angle measures. $\angle{ABD}$ = ($16(\frac{88}{17}) + 4)^{\circ}$ = $(\frac{1408}{17} + \frac{68}{17})^{\circ} = (\frac{1476}{17})^{\circ} = 86.82^{\circ}$ approximately.

$\angle{ABC} = 18x^{\circ} = 18(\frac{88}{17})^{\circ} = (\frac{1584}{17})^{\circ} = 93.18^{\circ}$ approximately. Since the two angles sum up to $180^{\circ}$ they are supplementary angles.

Final Answer:

Equation: $16x + 4 + 18x = 180$ $x = \frac{88}{17}$ The angles are supplementary.

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