Question

In this quartz crystal, m∠A = 95°, m∠B = 125°, m∠E = m∠D = 130°, and ∠C ≅ ∠F ≅ ∠G. Find m∠F.

a) 130°
b) 125°
c) 95°
d) 90°

Answer 1

In the given quartz crystal, m∠A = 95°, m∠B = 125°, m∠E = m∠D = 130°, and ∠C ≅ ∠F ≅ ∠G. By using the information that ∠C ≅ ∠F and the fact that the sum of the angles in a triangle is 180°, we can find that ∠F is equal to 337.5°.

Step-by-step explanation:

In the given quartz crystal, we have m∠A = 95°, m∠B = 125°, m∠E = m∠D = 130°, and ∠C ≈ ∠F ≈ ∠G. We want to find m∠F.

Since ∠C ≈ ∠F, we can set them equal to each other:

∠C = ∠F

Also, since ∠C + ∠F + ∠G = 180° and ∠G = 130°, we can substitute and solve for ∠F:

∠C + ∠F + 130° = 180°

2∠F + 95° + 130° = 180°

2∠F = -45°

∠F = -22.5° = 337.5°

Therefore, m∠F = 337.5°.