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Math  /  Geometry

QuestionEn la figura, m∠1=(8x)∘m \angle 1=(8 x)^{\circ} y m∠2=(x−9)∘m \angle 2=(x-9)^{\circ}. (a) Escribir una ecuación para hallar xx. Usar el signo de " = " en la respuesta.
Ecuación: □\square (b) Calcular la medida en grados de cada ángulo. m∠1=□∘m∠2=□∘\begin{array}{l} m \angle 1=\square^{\circ} \\ m \angle 2=\square^{\circ} \end{array}

Studdy Solution

STEP 1

1. Angles on a straight line are supplementary, meaning their measures add up to 180∘ 180^\circ .
2. m∠1=(8x)∘ m \angle 1 = (8x)^\circ and m∠2=(x−9)∘ m \angle 2 = (x-9)^\circ .

STEP 2

1. Write the equation for x x .
2. Solve for x x .
3. Calculate the measure of each angle.

STEP 3

Since angles on a straight line are supplementary, we have:
m∠1+m∠2=180∘ m \angle 1 + m \angle 2 = 180^\circ
Substitute the given expressions:
(8x)+(x−9)=180 (8x) + (x - 9) = 180

STEP 4

Combine like terms in the equation:
8x+x−9=180 8x + x - 9 = 180
9x−9=180 9x - 9 = 180

STEP 5

Add 9 9 to both sides to isolate the term with x x :
9x−9+9=180+9 9x - 9 + 9 = 180 + 9
9x=189 9x = 189

STEP 6

Divide both sides by 9 9 to solve for x x :
x=1899 x = \frac{189}{9}
x=21 x = 21

STEP 7

Substitute x=21 x = 21 back into the expressions for each angle:
m∠1=(8×21)∘ m \angle 1 = (8 \times 21)^\circ
m∠1=168∘ m \angle 1 = 168^\circ

STEP 8

Calculate m∠2 m \angle 2 :
m∠2=(21−9)∘ m \angle 2 = (21 - 9)^\circ
m∠2=12∘ m \angle 2 = 12^\circ
The equation to find x x is:
Ecuación: 8x+(x−9)=180 8x + (x - 9) = 180
The measures of the angles are:
m∠1=168∘m∠2=12∘ \begin{array}{l} m \angle 1 = 168^\circ \\ m \angle 2 = 12^\circ \end{array}

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