Answer:
Smaller angles = 39 degrees
Larger angles = 51 degrees
Explanations:
The sum of complementary angles is equal to 90 degrees.
Since the three support beams for a bridge form a pair of complementary angles, hence;
[tex](3x+3)+(5x-9)=90[/tex]
Simplify and get the value of "x"
[tex]\begin{gathered} 3x+5x+3-9=90 \\ 8x-6=90 \\ 8x=90+6 \\ 8x=96 \\ x=\frac{96}{8} \\ x=12 \end{gathered}[/tex]
Determine the smaller angles
[tex]\begin{gathered} Smaller\text{ angle}=3x+3 \\ Smaller\text{ angle}=3(12)+3 \\ Smaller\text{ angle}=36+3 \\ Smaller\text{ angle}=39^0 \end{gathered}[/tex]
Determine the larger angle
[tex]\begin{gathered} larger\text{ angle}=5x-9 \\ larger\text{ angle}=5(12)-9 \\ larger\text{ angle}=60-9=51^0 \end{gathered}[/tex]
