Math / Geometry

QuestionIn the figure, $m \angle 1=(5 x)^{\circ}$ and $m \angle 2=(x-6)^{\circ}$ . (b) Find the degree measure of each angle. $\begin{array}{l} m \angle 1=\square^{\circ} \\ m \angle 2=\square^{\circ} \end{array}$ (a) Write an equation to find $x$ . Make sure you use an "=" sign in your answer.
Equation: $\square$
$\times$ 5

Studdy Solution

STEP 1

1. The two angles, $\angle 1$ and $\angle 2$ , form a right angle together.
2. A right angle measures $90^\circ$ .

STEP 2

1. Write an equation to find $x$ .
2. Solve the equation for $x$ .
3. Calculate the degree measure of each angle.

STEP 3

Since $\angle 1$ and $\angle 2$ form a right angle together, their measures add up to $90^\circ$ . Therefore, we can write the equation:
$(5x) + (x - 6) = 90$
Equation: $(5x) + (x - 6) = 90$

STEP 4

Combine like terms in the equation:
$5x + x - 6 = 90$ $6x - 6 = 90$

STEP 5

Add $6$ to both sides of the equation to isolate the term with $x$ :
$6x - 6 + 6 = 90 + 6$ $6x = 96$

STEP 6

Divide both sides by $6$ to solve for $x$ :
$\frac{6x}{6} = \frac{96}{6}$ $x = 16$

STEP 7

Substitute $x = 16$ back into the expressions for $m \angle 1$ and $m \angle 2$ to find their measures:
$m \angle 1 = (5x)^\circ = (5 \cdot 16)^\circ = 80^\circ$

STEP 8

Substitute $x = 16$ into the expression for $m \angle 2$ :
$m \angle 2 = (x - 6)^\circ = (16 - 6)^\circ = 10^\circ$
The degree measure of each angle is:
$m \angle 1 = 80^\circ$ $m \angle 2 = 10^\circ$

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Studdy Solution

STEP 1

1. The two angles, $\angle 1$ and $\angle 2$ , form a right angle together.
2. A right angle measures $90^\circ$ .

STEP 2

1. Write an equation to find $x$ .
2. Solve the equation for $x$ .
3. Calculate the degree measure of each angle.

STEP 3

Since $\angle 1$ and $\angle 2$ form a right angle together, their measures add up to $90^\circ$ . Therefore, we can write the equation:
$(5x) + (x - 6) = 90$
Equation: $(5x) + (x - 6) = 90$

STEP 4

Combine like terms in the equation:
$5x + x - 6 = 90$ $6x - 6 = 90$

STEP 5

Add $6$ to both sides of the equation to isolate the term with $x$ :
$6x - 6 + 6 = 90 + 6$ $6x = 96$

STEP 6

Divide both sides by $6$ to solve for $x$ :
$\frac{6x}{6} = \frac{96}{6}$ $x = 16$

STEP 7

Substitute $x = 16$ back into the expressions for $m \angle 1$ and $m \angle 2$ to find their measures:
$m \angle 1 = (5x)^\circ = (5 \cdot 16)^\circ = 80^\circ$

STEP 8

Substitute $x = 16$ into the expression for $m \angle 2$ :
$m \angle 2 = (x - 6)^\circ = (16 - 6)^\circ = 10^\circ$
The degree measure of each angle is:
$m \angle 1 = 80^\circ$ $m \angle 2 = 10^\circ$

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Studdy Solution

STEP 1

1. The two angles, ∠1 \angle 1 ∠1 and ∠2 \angle 2 ∠2, form a right angle together.2. A right angle measures 90∘ 90^\circ 90∘.

STEP 2

1. Write an equation to find x x x.2. Solve the equation for x x x.3. Calculate the degree measure of each angle.

STEP 3

Since ∠1 \angle 1 ∠1 and ∠2 \angle 2 ∠2 form a right angle together, their measures add up to 90∘ 90^\circ 90∘. Therefore, we can write the equation:(5x)+(x−6)=90 (5x) + (x - 6) = 90 (5x)+(x−6)=90Equation: (5x)+(x−6)=90 (5x) + (x - 6) = 90 (5x)+(x−6)=90

STEP 4

Combine like terms in the equation:5x+x−6=90 5x + x - 6 = 90 5x+x−6=90 6x−6=90 6x - 6 = 90 6x−6=90

STEP 5

Add 6 6 6 to both sides of the equation to isolate the term with x x x:6x−6+6=90+6 6x - 6 + 6 = 90 + 6 6x−6+6=90+6 6x=96 6x = 96 6x=96

STEP 6

Divide both sides by 6 6 6 to solve for x x x:6x6=966 \frac{6x}{6} = \frac{96}{6} 66x​=696​ x=16 x = 16 x=16

STEP 7

Substitute x=16 x = 16 x=16 back into the expressions for m∠1 m \angle 1 m∠1 and m∠2 m \angle 2 m∠2 to find their measures:m∠1=(5x)∘=(5⋅16)∘=80∘ m \angle 1 = (5x)^\circ = (5 \cdot 16)^\circ = 80^\circ m∠1=(5x)∘=(5⋅16)∘=80∘

STEP 8

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1. The two angles, $\angle 1$ and $\angle 2$ , form a right angle together.
2. A right angle measures $90^\circ$ .

1. Write an equation to find $x$ .
2. Solve the equation for $x$ .
3. Calculate the degree measure of each angle.

Since $\angle 1$ and $\angle 2$ form a right angle together, their measures add up to $90^\circ$ . Therefore, we can write the equation:
$(5x) + (x - 6) = 90$
Equation: $(5x) + (x - 6) = 90$

Combine like terms in the equation:
$5x + x - 6 = 90$ $6x - 6 = 90$

Add $6$ to both sides of the equation to isolate the term with $x$ :
$6x - 6 + 6 = 90 + 6$ $6x = 96$

Divide both sides by $6$ to solve for $x$ :
$\frac{6x}{6} = \frac{96}{6}$ $x = 16$

Substitute $x = 16$ back into the expressions for $m \angle 1$ and $m \angle 2$ to find their measures:
$m \angle 1 = (5x)^\circ = (5 \cdot 16)^\circ = 80^\circ$