Question

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

Answer 1

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}`

Answer 2

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°