Question

in the triangle below, with right angle ∠d, suppose that m∠c = (4x − 3)° and m∠e = (2x + 39)°. find the degree measure of each angle in the triangle. m∠c = \\(\square\\)° m∠d = \\(\square\\)° m∠e = \\(\square\\)°

Explanation:

Step1: Usar la suma de ángulos en un triángulo

En un triángulo, la suma de los ángulos es \(180^{\circ}\). Aquí, \(\angle D = 90^{\circ}\), \(\angle C=(4x - 3)^{\circ}\) y \(\angle E=(2x + 39)^{\circ}\). Entonces:

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Step2: Resolver para \(x\)

Restar \(126\) de ambos lados:

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Dividir por \(6\):

$$ x=\frac{54}{6}=9 $$

Step3: Calcular \(m\angle C\)

Sustituir \(x = 9\) en \(\angle C=(4x - 3)^{\circ}\):

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Step4: Calcular \(m\angle E\)

Sustituir \(x = 9\) en \(\angle E=(2x + 39)^{\circ}\):

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Answer:

\(m\angle C = 33^{\circ}\), \(m\angle D=90^{\circ}\), \(m\angle E = 57^{\circ}\)