Question

1. in △lmn below, an angle bisector for each of its angles has been drawn. it is known that (overline{lm}congoverline{ln}). based on this information, which of the following must be a right angle? (1) (∠nem) (2) (∠nmg) (3) (∠mgn) (4) (∠lfm) 3. if the vertex angle of an isosceles triangle has a measure of (52^{circ}), then which of the following is the measure of one of its base angles? (1) (64^{circ}) (2) (68^{circ}) (3) (74^{circ}) (4) (128^{circ})

Explanation:

Pregunta 3

Step1: Propiedades de triángulo isósceles

En un triángulo isósceles, los ángulos de la base son iguales. La suma de los ángulos internos de un triángulo es \(180^{\circ}\). Sea \(x\) el ángulo de la base. Entonces \(52^{\circ}+2x = 180^{\circ}\).

Step2: Resolver la ecuación

Restar \(52^{\circ}\) de ambos lados: \(2x=180^{\circ}- 52^{\circ}=128^{\circ}\). Dividir por \(2\): \(x = \frac{128^{\circ}}{2}=64^{\circ}\).

Answer:

(1) \(64^{\circ}\)