Question

What is the value of x?

Answer 1

x=21

Explanation:

Hello There!

In order to find the value of x we need to find the value of y

The angle labeled y and the right angle are vertical angles with the angle labeled 5y +10 therefore they are congruent

so y+90=5y+10

step 1 subtract y from each side

5y-y=4y

now we have

90=4y+10

step 2 subtract each side by 10

90-10=80

now we have

80=4y

step 3 divide each side by 4

80/4=20

so y =20

now we plug in y to (5y+10)

5x20=100

100+10=110

So now we can find x

The angle labeled 3x+7 is supplementary with the angle that is equal to 110

meaning that the sum of the two angles equal 180

so 180 = 3x+110+7

step 1 combine like terms

110+117

now we have

180=3x+117

step 2 subtract each side by 117

180-117=63

now we have 3x=63

step 3 divide each side by 3

63/3=21

so we can conclude that x = 21

Answer 2

x = 21°

Explanation:

y = 180° - 90° - (3x+7)°

y = 83° - 3x

(5y + 10) and (3x + 7) are supplementary angles (their sum is 180°) so:

(5y + 10) + (3x + 7) = 180°

reduce:

5y + 3x = 163°

substitute for y:

5(83° - 3x) + 3x = 163°

415° - 15x + 3x = 163°

reduce:

-12x = -252

divide both sides by -12:

x = 21°

y = 83° - 3(21°) = 20°

check:

(5(20) + 10) + (3(21) + 7) = 180°

110° + 70° = 180°