3x 2x -5 x + 11 (4x + 7)° 90° (8x - 1)°

180° Every triangle has three angles. If you were to cut each angle out of the triangle and place them next to each other they would form a straight line. A line is 1800. Therefore the sum of the measures of the angles in a triangle is 180.

x + 11 + 2x - 5 + 3x 3x + 2x + x + 11 -5 6x + 6 Many times when we are finding the measurements of angles, the measurements are given to us in the form of expressions. We may need to combine expressions to solve for a measurement. When combining like terms, look for the terms that have the same variable and power then add their coefficients. Constants, or a term without a variable can be combined as well.

angle 1 + angle 2 + angle 3 ≠ 90° 1 2 3 Many times students get confused and think that the sum of the measures of the angles is 900, remember that when you cut out the angles it would create a straight line, which is 900

47 + 65 + x = 180 a 112 + x = 180 x = 68 angle b = 680 47° x 65° b c Sometimes we are asked to find the measure of an angle in a triangle. When we are given the other two angles it is best to set up an equation that is equal to 180 and solve for x. Find the measure of angle b. To find the measure of angle b first we have to find the value of x.

b X + 11 + 2x - 5 + 3x = 180 6x + 6 =180 6x = 174 x = 29 (2x -5)° c b a X + 11 + 2x - 5 + 3x = 180 6x + 6 =180 6x = 174 x = 29 Many times the angles of triangle are given to us as expressions. Find the measurement of angle a. Before you solve for angle a we need to find the value of x. You can set up an equation equal to 180 and solve for x.

Angle a = x + 11 Angle a = 29 + 11 Angle a = 400 (3x)° (x + 11)° c b a Once you have solved for x then you can substitute the x value into the expression and solve for the measure of the angle.

(8x + 2)° (4x)° (2x + 10)° m o n

65° 80° x a c b

(3x)° (2x – 11)° (2x + 27)° c b a

a c b