Question

PARALLELOGRAM QUESTION, LOTS OF POINTS! (i will report if you dont answer correctly)

Answer 1

We know that:

• Opposite angles in a parallelogram are equal.
• Sum of the angles in a quadrilateral always sum up to 360°

This means that:

• 
  `116x - 1 = 114x + 1`
• 
  `\angle C = \angle E`
• 
  `(116x - 1) + (114x + 1) + \angle C + \angle E = 360\°`

Step-1: Find the value of x.

`116x - 1 = 114x + 1`

`\rightarrow 116x - 114x = 1 + 1`

`\rightarrow 2x = 2`

`\rightarrow \bold{x = 1}`

Step-2: Solve for ∠C.

`(116x - 1) + (114x + 1) + \angle C + \angle C = 360\°`

`\rightarrow (116x - 1) + (114x + 1) + \angle C + \angle E = 360\°` [∠C = ∠E]

`\rightarrow 116x - 1 + 114x + 1 + 2\angle C = 360\°`

`\rightarrow 230x + 2\angle C = 360\°`

`\rightarrow 230(1) + 2\angle C = 360\°` [x = 1]

`\rightarrow 230 + 2\angle C = 360\°`

`\rightarrow 2\angle C = 360 - 230`

`\rightarrow 2\angle C = 130`

`\rightarrow \boxed{\bold{\angle C = (130)/(2) = 65\°}}`

Answer 2

65°

Explanation:

• opposite angles of a parallelogram are of equal measure.

solve for x:

116x - 1 = 114x + 1

116x - 114x = 1 + 1

2x = 2

x = 1

Find angle C:

• The base angles in parallelogram sum up to 180°

m∠C + 116(1) - 1 = 180°

m∠C = 180° - 115

m∠C = 65°