Question

malia makes a fabric design by drawing diagonals between opposite corners. she wants to draw other lines parallel to one of the diagonal lines, as shown by the dashed lines.
a. what should ∠1 be in order for line b to be parallel to line a? explain.
b. what should ∠2 be in order for line c to be parallel to line b? explain.
a. by the if two lines and a transversal form angles that are then the lines are parallel. therefore, ∠1 must be to the angle with measure 125°, meaning ∠1 must have a measure of °. (type a whole number.)

Explanation:

Step1: Identificar el teorema de ángulos correspondientes

Si dos líneas son paralelas y se cortan por una transversal, los ángulos correspondientes son iguales.

Step2: Encontrar el valor de ∠1

Para que la línea b sea paralela a la línea a, ∠1 y el ángulo de 125° son ángulos correspondientes. Entonces ∠1 = 125°.

Step3: Encontrar el valor de ∠2

Para que la línea c sea paralela a la línea b, ∠2 y el ángulo adyacente al de 125° son ángulos correspondientes. El ángulo adyacente al de 125° mide 180° - 125° = 55°. Entonces ∠2 = 55°.

Answer:

a. By the corresponding - angles theorem, if two lines and a transversal form corresponding angles that are equal, then the lines are parallel. Therefore, ∠1 must be equal to the angle with measure 125°, meaning ∠1 must have a measure of 125°.
b. The angle adjacent to the 125° angle measures 180 - 125=55°. By the corresponding - angles theorem, if two lines and a transversal form corresponding angles that are equal, then the lines are parallel. So ∠2 must be 55°.