Question

In the figure, m∠1=(x+14) ° and m∠2=(3x) ° . (a) Write an equation to find x. Male sure you use an “ = " sign in your answer.(b) Find the degree measure of each angle. Use the figure given in the picture to answer the questions.

Answer 1

The image is given below

From the image above, the angle is a right angle

Hence

The sum of the measure of angle 1 and measure of angle 2 is 90 degrees

i.e

`\begin{gathered} \angle1+\angle2=90^0 \\ \text{where } \\ \angle1=(x+14)^0,\angle2=(3x)^0 \end{gathered}`

Substitute the expression for angle 1 and angle 2, we obtain

`(x+14)^0+(3x)^0=90^0`

Simplifying the equation we have

`\begin{gathered} x+3x+14=90 \\ 4x+14=90 \\ \text{subtract 14 from both sides of the equation } \\ 4x+14-14=90-14 \\ 4x=76 \end{gathered}`

Hence, the equation to find x is

4x=76

To find the measure of each angle we need the know the value of x

`\begin{gathered} \text{from } \\ 4x=76 \\ \text{divide both sides by 4} \\ x=(76)/(4)=19 \\ \end{gathered}`

Hence the value of x is 19

Hence the measure of angle 1 will be

`\angle1=(x+14)^9=(19+14)^0=33^0`

The measure of angle 1 is 33°

Similarly, we substitute x for the measure of angle 2

`\angle2=3x^0=3(19)=57^0`

The measure of angle 2 is 57°