Question

In the image shown, line n is a transversal cutting parallel lines l and m. ∠1 = 3x + 18 ∠7 = 2x + 39 What is the measure of ∠7? A) 79° B) 81° C) 83° D) 86°

Answer 1

Answer:

b balty brings

Step-by-step explanation:

Answer 2

Answer:

B) 81°

Step-by-step explanation:

Given:

From the figure given below,

∠1 = 3x + 18

∠7 = 2x + 39

∠1  and ∠7 are a pair of exterior alternate angles. For two parallel lines l and m, cut by a transversal n, the pair of exterior alternate angles are congruent to each other.

Therefore, the angles 1 and 7 are congruent to each other. This gives,

∠1  ≅ ∠7

$3x+18=2x+39\\\\3x-2x=39-18\\\\x=21$

Therefore, the value of 'x' is 21.

Now, the measure of angle 7 can be calculated by plugging in the value of 'x' in the expression for angle 7. This gives,

$\angle 7 = 2x + 39\\\\\angle 7 =2\times 21+39\\\\\angle 7 =42+29\\\\\angle 7 =81\°$

Therefore, the correct option is option (B).