Find the measure of each angle in Triangle ABC.
m∠a=(40x−21)°m∠b=(31−2x)°m∠c=(x+14)°
since they add up to 180°, you have
40x-21 + 31-2x + x+14 = 180
x=4
Now figure the angle measures.
To find the measure of each angle in Triangle ABC, we need to solve the equation for x and substitute it back into each angle measure.
Given:
m∠a = (40x - 21)°
m∠b = (31 - 2x)°
m∠c = (x + 14)°
To find x, we can set up the equation:
m∠a + m∠b + m∠c = 180° (sum of angles in a triangle)
Substituting the given angle measures:
(40x - 21) + (31 - 2x) + (x + 14) = 180
Simplifying the equation:
40x - 21 + 31 - 2x + x + 14 = 180
39x + 24 = 180
39x = 180 - 24
39x = 156
x = 156/39
x = 4
Now, substituting the value of x back into each angle measure:
m∠a = (40(4) - 21)°
m∠b = (31 - 2(4))°
m∠c = (4 + 14)°
Simplifying each angle measure:
m∠a = (160 - 21)° = 139°
m∠b = (31 - 8)° = 23°
m∠c = (18)° = 18°
Therefore, the measure of each angle in Triangle ABC is:
m∠a = 139°
m∠b = 23°
m∠c = 18°
To find the measure of each angle in Triangle ABC, you need to set up equations and solve for the value of x.
Given:
m∠a = (40x - 21)°
m∠b = (31 - 2x)°
m∠c = (x + 14)°
The sum of the angles in a triangle is always 180°. So, we can set up an equation using the given angles:
m∠a + m∠b + m∠c = 180°
Substituting the given expressions for each angle:
(40x - 21) + (31 - 2x) + (x + 14) = 180°
Now, let's solve this equation:
40x - 21 + 31 - 2x + x + 14 = 180
39x + 24 = 180
39x = 180 - 24
39x = 156
x = 156 / 39
x = 4
Now that we have the value of x, we can substitute it back into the expressions for each angle to find their measures:
m∠a = (40x - 21)°
m∠a = (40 * 4 - 21)°
m∠a = 159°
m∠b = (31 - 2x)°
m∠b = (31 - 2 * 4)°
m∠b = 23°
m∠c = (x + 14)°
m∠c = (4 + 14)°
m∠c = 18°
Therefore, the measure of angle A is 159°, angle B is 23°, and angle C is 18° in Triangle ABC.