(8×+5)° (5×-1)° (4x+6)°
Use the Triangle Angle Sum Theorum to find the measures of each angle for the triangle shown in the diagram.
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Let's find the measures of each angle one by one:
Angle 1: 8x + 5 degrees
Angle 2: 5x - 1 degrees
Angle 3: 4x + 6 degrees
To find the sum of the angles, we add the measures together:
(8x + 5) + (5x - 1) + (4x + 6)
This simplifies to:
17x + 10
Since the sum of the angles in a triangle is always 180 degrees, we set up the equation:
17x + 10 = 180
To solve for x, we isolate it by subtracting 10 from both sides:
17x = 170
Then, we divide both sides by 17:
x = 10
Now, we can find the measures of each angle by substituting x = 10 into the expressions:
Angle 1: 8(10) + 5 = 85 degrees
Angle 2: 5(10) - 1 = 49 degrees
Angle 3: 4(10) + 6 = 46 degrees
So, the measures of each angle of the triangle are:
Angle 1 = 85 degrees
Angle 2 = 49 degrees
Angle 3 = 46 degrees