Question

You are making a picture frame in shop class. Two pieces of wood are cut to form complementary angles so they fit together properly . One angle needs to be (7x +23) and the other angle needs to be (3x +27). What is the measure of the larger angle?

Answer 1

Answer:

The larger angle is;

$51^{\circ}$

Explanation:

Given that the two woods are cut to form complementary angles.

Recall that complementary angles add up to 90 degrees.

Given the two angles as;

$(7x+23)^{\circ}+(3x+27)^{\circ}=90^{\circ}$

Solving the equation for x;

$\begin{gathered} 7x+23+3x+27=90 \\ 7x+3x+23+27=90 \\ 10x+50=90 \\ 10x=90-50 \\ 10x=40 \\ \text{divide both sides by 10;} \\ \frac{10x}{10}=\frac{40}{10} \\ x=4 \end{gathered}$

Since we have the value of x, we can the substitute to find the values of each angle;

$\begin{gathered} (7x+23)^{\circ} \\ (7(4)+23)^{\circ} \\ (28+23)^{\circ} \\ =51^{\circ} \\ \\ (3x+27)^{\circ} \\ (3(4)+27)^{\circ} \\ (12+27)^{\circ} \\ =39^{\circ} \end{gathered}$

Therefore, form the values of the two angles, the larger angle is;

$51^{\circ}$