find the measures of the angles labeled in the figure below. measure of angle EFD=measure of angle EHF=measure of angle HFG=measure of angle G=

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03-11-2022
Mathematics

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find the measures of the angles labeled in the figure below. measure of angle EFD=measure of angle EHF=measure of angle HFG=measure of angle G=

Sagot :

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NehalM64983idn NehalM64983idn · Answer 1 · 2022-11-03T09:15:37-04:00

EXPLANATION:

We must bear in mind that the internal angles of a triangle must add up to 180 degrees.

We will first find values of unknown angles and finally add to find the corresponding measures.

[tex]\begin{gathered} To\text{ find F:} \\ corresponds\text{ }to\text{ the same angle }measure\text{ }54(F) \\ To\text{ find G:} \\ We\text{ add }the\text{ two internal }angles\text{ 54 }and\text{ s}ubtract\text{ }180\colon \\ 54+54=180 \\ 180-54-54 \\ 180-108 \\ 72\text{ ( }angle\text{ G)} \\ To\text{ find E;} \\ We\text{ must }the\text{ measures }H\text{ and G} \\ H=54\text{ ; G= 72 E=X} \\ 54+72=180 \\ 180-54-72 \\ 54(\text{Angle E)} \\ To\text{ find D} \\ We\text{ must the measures: 33 +54 and }substract\text{ 180} \\ 33+54=180 \\ 180-33-54 \\ 93\text{ (angle D)} \end{gathered}[/tex]

Now to find the measurements given in the exercise; We must take the values found according to what each exercise asks for and add them.

[tex]\begin{gathered} \text{Measure of angle EFD:} \\ E(54)+\text{ F(54})+D(93)=201 \\ \text{Measure of angle EHF:} \\ E(54)+H(54)+F(54)=162 \\ \text{Measure of angle HFG:} \\ H(54)+F(54)+G(72)=180 \\ \text{Measure of angle G:} \\ G=\text{ 72 degr}ees \end{gathered}[/tex]

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