In the figure, c ∥ d. What are the measures of ∠1 and ∠2? Enter your answers in the boxes.

<1=105°

<2=75°

Step-by-step explanation:

The value of angles 1 and 2 can be determined as follows

given that c||d

The two  parallel lines c and d are intersected by a transversal.

75° and <2 are corresponding angles and thus will be equal.

<2=75°

<1 and <2 are angles along the same line.

<1+<2=180°

<1=180-<2=180-75=105°

<1=105°

<2=75°

Measure of angle 1 is  (∠1 = 105° ) and angle 2 is ( ∠2 = 75° ) .

Step-by-step explanation:

We have,  c ∥ d in the above figure . Corresponding angles are angles that are in the same relative position at an intersection of a transversal and at least two lines. In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points , in this case the line crossing other two parallel lines is transversal. If the lines are parallel then the corresponding angles are congruent.

By corresponding angle property,  ∠6 = ∠2  , ∴∠2 = 75°

We know that in line c sum of ∠1 + ∠2 = 180°  

⇒ ∠1 = 180°-∠2 ⇒ 180° - 75° ⇒ ∠1 = 105°

∴Measure of angle 1 ( ∠1 ) and angle 2 ( ∠2 ) is 105° & 75° respectively.