Find the measure of each marked angle. See Example 2 supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees

Verified step by step guidance

1. Recall that supplementary angles are two angles whose measures add up to 180 degrees. This means we can write the equation: \( (10\times x + 7) + (7\times x + 3) = 180 \).
2. Combine like terms on the left side of the equation: \( 10x + 7 + 7x + 3 = 180 \) becomes \( 17x + 10 = 180 \).
3. Isolate the variable term by subtracting 10 from both sides: \( 17x = 180 - 10 \) which simplifies to \( 17x = 170 \).
4. Solve for \( x \) by dividing both sides by 17: \( x = \frac{170}{17} \).
5. Once you find \( x \), substitute it back into each angle expression to find the measure of each angle: \( 10x + 7 \) and \( 7x + 3 \).

Key Concepts

Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. This relationship is fundamental when solving for unknown angle measures given algebraic expressions representing each angle.

Setting Up and Solving Linear Equations

To find the value of x, set up an equation where the sum of the two angle expressions equals 180. Solving this linear equation involves combining like terms and isolating x to determine its value.

Substitution to Find Angle Measures

After finding x, substitute its value back into the original expressions to calculate the exact measures of each angle. This step ensures the solution is complete and verifies the angles are supplementary.