Algebraic Equation: x+(2/3x-15)=180 Measures of the Angles: 117^(∘) and 63^(∘)
Practice makes perfect
Let's call the unknown angles ∠ A and ∠ B. We know that ∠ A and ∠ B form a linear pair, and, therefore, they are supplementary angles. Since the sum of measures of supplementary angles is 180^(∘), we can write an equation.
m∠ A + m∠ B = 180^(∘)
We are told that the measure of one angle is 15^(∘) less than 23 the measure of the other angle. Assume that the measure of ∠ A is x. We then have the following expressions for the measures of the unknown angles.
m∠ A =& x [0.5em]
m∠ B =& 2/3x- 15
Substituting these values into the sum gives us the desired algebraic equation.
m∠ A+ m∠ B&=180
x+ (2/3x-15)&=180
Now we can solve for x and find the measures of the angles.
