Answered

1. An angle measures 15 degrees more than twice its supplement.Find the measure of the supplement.
2. 2 angles are complementary.One contains 30 degrees more than the other.Find both angles.
3. 2 angles of a triangle have equal measures,but the 3rd angle measure s 36 degrees less than the sun of the other two.Find the measurement of each angle of the triangle.

Sagot :

1. 55°
2. 30°, 60°
3. 72° 72° 36°
1. angle's supplement = x
   the angle = 2x + 15
   sum of the measure of supplementary angles = 180

Equation: x + 2x + 15 = 180
              3x = 180 - 15
              3x/3 = 165
              x = 55 degrees  the measure of the angle's supplement

2.  Let angle's complement is x
     the angle = x + 30
     sum of the measures of complementary angles = 90
     Equation:  x + x+30 = 90
                     2x = 90 - 30
                     2x/2 = 60/2
                      x = 30, the measure of the first angles
                      x + 30 = 30 + 30 = 60, measure of the other angle

60 degrees and 30 degrees are the measures of complementary angles.

3.  sum of the measure of the angles of triangle is 180 degrees.

The firs and second angles are equal in measure
x + x = 2x, the total of the two equal angles

2x - 36 , the measure of the third angle.

Equation:
2x + 2x - 36 = 180
4x - 36 = 180
4x = 180 + 36
4x/4 = 216
x = 54

the measure of two angles are 54 degrees each.

To get the measure of the third angle:
2(54) - 36 = third angle
108 - 36 =  72 degress

The measure of the angles of the triangle are:
54 degrees, 54 degrees, and 72 degrees.  Their total is 180 degrees.