Measure of one of the vertical angle is 156°
Solution:
The measure of angles given are (x + 104)° and 3x°.
The given angles are vertical in order.
If two lines meet at a point, then the angle formed in vertical positions are equal.
That is vertically opposite angles are equal.
⇒ 3x° = (x + 104)°
⇒ 3x° = x° + 104°
Subtract x° on both sides of the equation to equal the expression,
⇒ 3x° – x° = x° + 104° – x°
⇒ 2x° – x° = 104°
⇒ 2x° = 104°
Divide both sides of the expression by 2, we get
⇒ x° = 52°
Substitute x° = 52° in one of the vertical angle.
3x° = 3 × 52° = 156° (or)
x° + 104° = 52°+ 104° = 156°
Hence the measure of one of the vertical angle is 156°.
