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)

Step-by-step 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.

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

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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.