Angle F and angle H are supplementary angles.
The measure of angle F is 77°
The measure of angle H is (5x + 18)°
Which equation can be used to find the value of x?
A. 77 = 5x + 18
B. 77+ (5x + 18) = 180
C. 77+ (5x + 18 = 90
D. 77+ (5x + 18) = 360
Supplementary angles are two angles with a sum of 180°.
If angle F and angle H are supplementary angles then:
F + H = 180°
F = 77°
H = ( 5 x + 18 )°
so
F + H = 180°
77° + ( 5 x + 18 )° = 180°
Answer B.
To find the value of x, we can use the fact that angle F and angle H are supplementary angles. Supplementary angles add up to 180 degrees.
Given that the measure of angle F is 77° and the measure of angle H is (5x + 18)°, we can set up the equation:
Angle F + Angle H = 180
Substituting the values, we have:
77 + (5x + 18) = 180
Simplifying further:
77 + 5x + 18 = 180
Combining like terms:
95 + 5x = 180
Now, to isolate x, we can subtract 95 from both sides:
95 + 5x - 95 = 180 - 95
5x = 85
Dividing both sides by 5:
5x/5 = 85/5
x = 17
Therefore, the equation that can be used to find the value of x is A. 77 = 5x + 18.
The correct equation that can be used to find the value of x is option B.
Explanation:
Since angle F and angle H are supplementary angles, their sum should be equal to 180 degrees.
The measure of angle F is given as 77°, so angle H can be represented as (5x + 18)°.
Therefore, the equation becomes:
77 + (5x + 18) = 180
Simplifying this equation gives us the correct option B.