Consider the following figure to answer questions below:

Consider Rectangle LOVE

1.If LV = 30 cm, how long is OE?
2.If EO = 25 cm, how long is EM?
3.If m∠2 = 38°, find the measurement of ∠1?

Consider Rhombus BASE

4.If BO = 12 cm, how long is BS?
5.If m∠OBE = 45°, find the measure of ∠1,∠2,and ∠3.

Question

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Rosiearerose05viz Rosiearerose05viz · Answer 1

Answer:

1) OE = 30cm 3) ∠1 = 52° 5) ∠1 = 45°, ∠2 = 45°, ∠3 = 90°

2) EM = 12.5cm 4) BS = 24cm

Step-by-step explanation:

1) - 3)

Since the given figure is a rectangle the diagonal are equal length

If LV = 30, OE = 30cm

EO = 25cm, EM [tex]\frac{25}{2}[/tex] = 12.5cm

m∠2 = 38° ∠1 = 90 - 38

= 52°

4) BO = 12 cm

BS = 12 + 12 = 24cm

Since AE bisects line BS,

BO = OS = 12

BS = BO + OS

BS = 12 + 12 = 24cm

5) If m∠OBE = 45°

m∠OBA is also 45°

Since OS bisects angle ABE

m∠OBE = m∠OBA = 45°

m∠BOA = 90°

since BS ⊥ AE

∠OAB = 180 - (90 + 45)

= 45°

∠1 = 45°, ∠2 = 45°, ∠3 = 90°