Question

find the value of x.
3)
4)
5)

Explanation:

Step1: Use the triangle angle - sum property for problem 3

The sum of angles in a triangle is \(180^{\circ}\).
So, \((x + 70)+50 + 70=180\)

$$x+70+50 + 70=180$$

$$x+190 = 180$$

$$x=180 - 190$$

$$x=- 10$$

(This is wrong, likely a mis - label. Assuming the triangle has angles \(x\), \(50^{\circ}\), \(70^{\circ}\). Then \(x+50 + 70=180\), \(x=180-(50 + 70)=60\))

Step2: Use the triangle angle - sum property for problem 4

The sum of angles in a triangle is \(180^{\circ}\).
\(2x + 2+3x+133 = 180\)
Combine like terms: \(5x+135 = 180\)
Subtract 135 from both sides: \(5x=180 - 135\)

$$5x=45$$

Divide both sides by 5: \(x = 9\)

Step3: Use the exterior - angle property for problem 5

The exterior - angle property states that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
\(\angle BDC=180 - 120=60^{\circ}\) (linear pair)
\(8x=10 + 3x+60\) (exterior - angle property: \(\angle BDC\) is non - adjacent to \(\angle C\) and \(\angle B\))
Subtract \(3x\) from both sides: \(8x-3x=10 + 60\)

$$5x=70$$

Divide both sides by 5: \(x = 14\)

Answer:

1. \(x = 60\)
2. \(x = 9\)
3. \(x = 14\)