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Solve for × and then find the missing angle in
the triangle below. SHOW ALL WORK.

Solve for × and then find the missing angle in the triangle below. SHOW ALL WORK.-example-1

2 Answers

4 votes

Answer:

The value of x is 4.

  • ∠E = 62⁰
  • ∠G = 28⁰
  • ∠O = 90⁰

Step-by-step explanation:

As we know that the sum of interior angles of triangle is 180⁰.

So, adding all the given sides and subtracting to 180⁰, to find the value of x.


\begin{gathered} \quad{\implies{\sf{Sum\:of\:all\: angles={180}^(\circ)}}}\\\\\quad{\implies{\tt{6x + {38}^(\circ) + {90}^(\circ) +5x + {8}^(\circ) = {180}^(\circ)}}}\\\\\quad{\implies{\tt{(6x + 5x) + ({38}^(\circ) + {90}^(\circ) + {8}^(\circ)) = {180}^(\circ)}}}\\\\\quad{\implies{\tt{(11x) + ({128}^(\circ) + {8}^(\circ)) = {180}^(\circ)}}}\\\\\quad{\implies{\tt{(11x) + ({136}^(\circ)) = {180}^(\circ)}}}\\\\\quad{\implies{\tt{11x + {136}^(\circ) = {180}^(\circ)}}}\\\\\quad{\implies{\tt{11x = {180}^(\circ) - {136}^( \circ)}}}\\\\\quad{\implies{\tt{11x = {44}^( \circ)}}}\\\\\quad{\implies{\tt{x = (44)/(11)}}}\\\\\quad{\implies{\tt{\underline{\underline{x = 4}}}}}\end{gathered}

Hence, the value of x is 4.

Now, we know the value of x. So, calculating the mission angles of triangle :

  • ➠ ∠E = 6x+38⁰ = 6×4+38 = 62⁰
  • ➠ ∠G = 5x+8⁰ = 5×4+8 = 28⁰
  • ➠ ∠O = 90⁰


\rule{300}{2.5}

User Yonatanmn
by
8.0k points
7 votes

Answer:

x = 4°

Explanation:

all angles in a triangle sum up to 180°

6x + 38° + 5x + 8° + 90° = 180 °

11x +136° = 180°

11x = 44°

x = 4°

User Sir Robert
by
8.5k points

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