∠a and ∠b are vertical angles with m∠a=x and m∠b=5x−80 .

what is m∠a ?

The measure angle A is .

Step-by-step explanation:

Given Information:

According to the Vertical Angle Theorem, the two opposite vertical angles are congruent due to the intersection of two lines.

Therefore, equating  we get,

Therefore, the measure angle A is .

For more information, refer to the link:

link

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always congruent to one another

in this problem

∠A and ∠B are vertical angles

so

∠A=∠B

we have

∠A= 

∠B=

equate angle A and angle B

solve for x

therefore

the answer is

the measure of angle A is

check the picture below.

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.