Use the Triangle Angle Sum Theorem to find the third angle of a triangle if the other two angles measure 25° and 68°.
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180°.
So we can set up the equation:
(5x + 4) + (4x + 14) + (6x - 3) = 180°
Simplifying:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now we can substitute x = 11 into the expressions for each angle to find their measures:
Angle 1: 5x + 4 = 5(11) + 4 = 59°
Angle 2: 4x + 14 = 4(11) + 14 = 58°
Angle 3: 6x - 3 = 6(11) - 3 = 63°
Therefore, the measures of the angles for the triangle are 59°, 58°, and 63°.
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180°.
Let's use this theorem to find the measure of the third angle:
x + 25° + 68° = 180° (x is the measure of the third angle)
Simplifying the equation:
x + 93° = 180°
Subtracting 93° from both sides:
x = 87°
Therefore, the third angle of the triangle measures 87°.
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
(8x + 5) (5x - 1) (4x + 6)
(1 point)
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180°.
Let's use this theorem to find the measures of the angles in the triangle:
(8x + 5) + (5x - 1) + (4x + 6) = 180°
Simplifying the equation:
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing by 17:
x = 10
Now we can substitute x = 10 into the expressions for each angle to find their measures:
Angle 1: 8x + 5 = 8(10) + 5 = 85°
Angle 2: 5x - 1 = 5(10) - 1 = 49°
Angle 3: 4x + 6 = 4(10) + 6 = 46°
Therefore, the measures of the angles in the triangle are 85°, 49°, and 46°.
The angles of a triangle measure (x+10)°, (x+20)°, and (x+30)°. Find the measure of the smallest angle.
The angles of a triangle always add up to 180 degrees.
So (x+10)° + (x+20)° + (x+30)° = 180°.
Simplifying the left side of the equation:
3x + 60 = 180
Subtracting 60 from both sides:
3x = 120
Dividing both sides by 3:
x = 40
Now we can find the measure of the smallest angle:
x + 10 = 40 + 10 = 50
Therefore, the measure of the smallest angle is 50 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
5x + 4
4x + 14
6x - 3