Question

Quadrilateral DEFG is a rhombus and m value of p

Answer 1

Note that:

• Opposite angles are always equal.
• The sum of the degrees in a quadrilateral is 360°

This means that:

• ∠F = ∠D = 62°
• ∠E = ∠G = 5p + 49
• ∠F + ∠D + ∠E + ∠G = 360

Solving for p.

• ∠F + ∠D + ∠E + ∠G = 360
• => 62 + 62 + 5p + 49 + 5p + 49 = 360
• => p(5 + 5) + (62 + 62 + 49 + 49) = 360
• => p(10) + (222) = 360
• => 10p + 222 = 360
• => 10p = 360 - 222
• => 10p = 138
• => 10p/10 = 138/10
• => p = 13.8

Check:

• ∠E = ∠G = 5p + 49
• => ∠E = ∠G = 5(13.8) + 49
• => ∠E = ∠G = 69 + 49
• => ∠E = ∠G = 118°
• => ∠F + ∠D + ∠E + ∠G = 360
• => 62 + 62 + 118 + 118 = 360
• => 360 = 360 (True)