Use the Triangle Angle Sum Theorem to find the third angle of a triangle if the other two angles measure 25° and 68°.

Answer 1

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°.

Answer 2

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)

Answer 3

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°.

Answer 4

The angles of a triangle measure (x+10)°, (x+20)°, and (x+30)°. Find the measure of the smallest angle.

Answer 5

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.

Answer 6

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

Answer 7

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°.