Three support beams for a bridge form a pair of complementary angles. Find the measure of each angle.Smaller angles:Larger angles:

Question

asked Dec 12, 2023 175k views

1 Answer

Jeff Werner · Answer 1 · 2023-12-16T04:14:16+0000

Smaller angles = 39 degrees

Larger angles = 51 degrees

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;

Simplify and get the value of "x"

$\begin{gathered} 3x+5x+3-9=90 \\ 8x-6=90 \\ 8x=90+6 \\ 8x=96 \\ x=(96)/(8) \\ x=12 \end{gathered}$

Determine the smaller angles

$\begin{gathered} Smaller\text{ angle}=3x+3 \\ Smaller\text{ angle}=3(12)+3 \\ Smaller\text{ angle}=36+3 \\ Smaller\text{ angle}=39^0 \end{gathered}$

Determine the larger angle

$\begin{gathered} larger\text{ angle}=5x-9 \\ larger\text{ angle}=5(12)-9 \\ larger\text{ angle}=60-9=51^0 \end{gathered}$