Question

in the triangle below, suppose that ( mangle l = (6x - 3)^circ ), ( mangle m = (4x - 4)^circ ), and ( mangle n = x^circ ). find the degree measure of each angle in the triangle. ( mangle l = square^circ ) ( mangle m = square^circ ) ( mangle n = square^circ )

Explanation:

Step1: Usar la suma de ángulos en un triángulo

La suma de los ángulos internos de un triángulo es \(180^{\circ}\). Entonces, \(x+(4x - 4)+(6x - 3)=180\).
Simplificar la ecuación: \(x + 4x-4+6x - 3=180\), \(11x-7 = 180\).

Step2: Resolver para \(x\)

Sumar \(7\) a ambos lados: \(11x=180 + 7=187\).
Dividir por \(11\): \(x=\frac{187}{11}=17\).

Step3: Calcular \(m\angle N\)

Como \(m\angle N=x^{\circ}\), entonces \(m\angle N = 17^{\circ}\).

Step4: Calcular \(m\angle M\)

Sustituir \(x = 17\) en \(m\angle M=(4x - 4)^{\circ}\). \(m\angle M=4\times17-4=68 - 4=64^{\circ}\).

Step5: Calcular \(m\angle L\)

Sustituir \(x = 17\) en \(m\angle L=(6x - 3)^{\circ}\). \(m\angle L=6\times17-3=102 - 3=99^{\circ}\).

Answer:

\(m\angle N = 17^{\circ}\), \(m\angle M = 64^{\circ}\), \(m\angle L = 99^{\circ}\)