Question

(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.

Answer 1

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