Question

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

Answer 1

Answer:

65°

step-by-step 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°

Answer 2

Solution:

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]

$\rightarrow 230 + 2\angle C = 360\°$                                                                          

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

$\rightarrow 2\angle C = 130$

$\rightarrow \boxed{\bold{\angle C = \frac{130}{2} = 65\°}}$