Question

Please help ! only G-J 15 points for this.

Answer 1

Answers: G) ∠BCS = 57.5°

H) ∠FHI = 72°

I) ∠ACB and also ∠DCH

J) ∠CHD (which can also be named ∠BHE)

Explanation:

First of all, I checked your answers for A-F and they are all correct. YAY!

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G) Draw a point halfway between B and D and label it S. Then draw a ray from C passing through S.

∠ACB and ∠BCD are supplementary so

65° + ∠BCD = 180°

⇒ ∠BCD = 115°

Since ray CS bisects ∠BCD, then ∠BCS is half of ∠BCD.

`\angle BCS=(1)/(2) (\angle BCD)\\\\. \quad \quad=(1)/(2)(115^o)\\\\. \quad \quad =\large\boxed{57.5^o}`

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H) The instructions state to draw a line from H to F. This divides ∠DHI into two angles: ∠FHD and ∠FHI. Since lines BI and EG are perpendicular, then ∠DHI = 90°. It is given that ∠FHI is 4 times larger than ∠FHD so we can use substitution...

∠FHD + ∠FHI = ∠DHI

∠FHD + 4(∠FHD) = 90°

5(∠FHD) = 90°

∠FHD = 18°

∠FHI = 4(∠FHD)

= 4 (18°)

=
`\large\boxed{72^o}`

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I) adjacent means they share a side and supplementary means they form a straight angle. There are two angles that are adjacent and supplementary to ∠ACH.

• ACB - they share side AC and are supplementary on BH

• DCH - they share side CH and are supplementary on AD

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J) congruent means equal and adjacent means they share a side.

The angle that is not congruent nor adjacent to ∠GHI is its vertical angle, which is ∠CHD. Notice that ∠CHD is the same as ∠BHE.