Use the Linear Pair Postulate to form two equations in one variable.
50^(∘), 130^(∘), 50^(∘), 130^(∘)
Practice makes perfect
Looking at the figure, we can identify four pairs of supplementary angles. However, only two of these pairs are written in terms of only one variable, x or y.
Supple&mentary angles:
&1. 10y^(∘) and (3y+11)^(∘)
&2. 10y^(∘) and (4x-22)^(∘)
&3. (7x+4)^(∘) and (3y+11)^(∘)
&4. (7x+4)^(∘) and (4x-22)^(∘)
We will use the first and the fourth pair to find the values of y and x, respectively. By definition, the measures of supplementary angles add up to 180^(∘). We will use the first pair of supplementary angles to form the equation that can be solved for y.
Having solved the equations, we can calculate the individual angles by substituting x= 18 and y= 13 into the given expressions.
(3* 13+11)^(∘) &=50^(∘)
10* 13^(∘) &=130^(∘)
(4* 18-22)^(∘) &=50^(∘)
(7* 18+4)^(∘) &=130^(∘)
