Question

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

Answer 1

Answer:

x = 4°

Step-by-step explanation:

all angles in a triangle sum up to 180°

6x + 38° + 5x + 8° + 90° = 180 °

11x +136° = 180°

11x = 44°

x = 4°

Answer 2

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.

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

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

$\rule{300}{2.5}$