Angle D and angle I are supplementary angles. Find the measure of both angles if m(angle sign)D = 3x + 8 m(angle sign) 2x = 18

To solve this problem, we need to first understand that supplementary angles add up to \(180^\circ\). 

Given:
- \(m(\angle D) = 3x + 8\)
- \(m(\angle I) = 2x + 18\)

Since these angles are supplementary:
\[
m(\angle D) + m(\angle I) = 180^\circ
\]

Substitute the given expressions:
\[
(3x + 8) + (2x + 18) = 180
\]

Now, combine like terms:
\[
3x + 2x + 8 + 18 = 180
\]
\[
5x + 26 = 180
\]

Next, solve for \(x\):
\[
5x = 180 - 26
\]
\[
5x = 154
\]
\[
x = \frac{154}{5}
\]
\[
x = 30.8
\]

Now, substitute \(x = 30.8\) back into the expressions for \(m(\angle D)\) and \(m(\angle I)\):

\[
m(\angle D) = 3(30.8) + 8 = 92.4 + 8 = 100.4^\circ
\]
\[
m(\angle I) = 2(30.8) + 18 = 61.6 + 18 = 79.6^\circ
\]

Thus, the measures of the angles are:
- \(m(\angle D) = 100.4^\circ\)
- \(m(\angle I) = 79.6^\circ\)

These angles add up to \(180^\circ\), confirming the solution is correct.

Would you like more details or have any questions?

Here are five related questions you might find useful:
1. What is the definition of complementary angles?
2. How do you solve for unknown angles in a triangle?
3. What happens when two angles are both equal and supplementary?
4. How do you find the measure of an angle in an isosceles triangle?
5. What is the relationship between adjacent angles and linear pairs?

**Tip:** Always double-check your calculations when dealing with algebraic expressions, especially when substituting values back into the equations.

Learn how to find the measures of supplementary angles D and I using algebraic equations. Step-by-step solution provided with calculations and verification. Suitable for high school students.

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