Questions: In the figure, m ∠1=(x-23)° and m ∠2=(6x)°. (a) Write an equation to find x. Make sure you use an "=" sign in your answer. Equation: (b) Find the degree measure of each angle. m ∠1=° m ∠2=°

In the figure, m ∠1=(x-23)° and m ∠2=(6x)°.
(a) Write an equation to find x. Make sure you use an "=" sign in your answer.

Equation:

(b) Find the degree measure of each angle.

m ∠1=°

m ∠2=°

Transcript text: In the figure, $m \angle 1=(x-23)^{\circ}$ and $m \angle 2=(6 x)^{\circ}$. (a) Write an equation to find $x$. Make sure you use an "=" sign in your answer. Equation: $\square$ (b) Find the degree measure of each angle. \[ \begin{array}{l} m \angle 1=\square^{\circ} \\ m \angle 2=\square^{\circ} \end{array} \]

Solution

Solution Steps

Step 1: Set up the equation

Angles 1 and 2 form a supplementary angle (180°). Therefore, the sum of their measures is 180°. This gives us the equation:

(x - 23) + 6x = 180

Step 2: Solve for x

Combine like terms:

7x - 23 = 180

Add 23 to both sides:

7x = 203

Divide both sides by 7:

x = 29

Step 3: Calculate angle measures

Substitute x = 29 back into the expressions for the angle measures:

m∠1 = (29 - 23)° = 6°

m∠2 = (6 * 29)° = 174°

Final Answer

(a) Equation: (x - 23) + 6x = 180

(b) m∠1 = 6° m∠2 = 174°

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