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

The larger angle is;

`51^(\circ)`

Step-by-step 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;} \\ (10x)/(10)=(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)`