Find the measure of each marked angle. See Example 2 supplementary angles with measures 6𝓍 - 4 and 8𝓍 - 12 degrees

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Recall that supplementary angles are two angles whose measures add up to 180 degrees. This means we can write the equation: \( (6\times x - 4) + (8\times x - 12) = 180 \).

Combine like terms on the left side of the equation: \( 6x - 4 + 8x - 12 = 180 \) becomes \( (6x + 8x) + (-4 - 12) = 180 \), which simplifies to \( 14x - 16 = 180 \).

Isolate the variable term by adding 16 to both sides: \( 14x - 16 + 16 = 180 + 16 \), which simplifies to \( 14x = 196 \).

Solve for \(x\) by dividing both sides by 14: \( x = \frac{196}{14} \).

Once you find \(x\), substitute it back into the expressions for each angle: \(6x - 4\) and \(8x - 12\) to find the measure of each marked angle.

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주요 개념

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Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. This relationship is fundamental when solving problems involving linear pairs or angles on a straight line. Knowing that the sum is always 180 degrees allows you to set up equations to find unknown angle measures.

Setting Up and Solving Linear Equations

When given algebraic expressions for angles, you can form an equation based on their relationship (e.g., supplementary angles sum to 180). Solving this linear equation for the variable x helps determine the exact angle measures. Mastery of basic algebraic manipulation is essential here.

Substitution to Find Angle Measures

After finding the value of the variable, substitute it back into the original expressions to calculate the actual angle measures. This step ensures you translate the algebraic solution into meaningful geometric information, completing the problem-solving process.