Answer:
[tex] \huge{ \boxed{ \bold{ \sf{ \pink{80°}}}}} [/tex]
Step-by-step explanation:
✰ [tex] \underline{ \sf{First, \: Let's \: learn \: about \: internal \: angles \: of \: a \: triangle}}[/tex]
The angles which are formed inside by the joining of arms of a triangle is called interior angles of a triangle. According to the figure provided , In ∆ ABC , ∠ABC , ∠ ACB , ∠ BAC are interior angles because they lie inside the ∆ ABC and sum of such interior angles is always 180°.
❀ [tex] \sf{Now, \: Let's \: solve} : [/tex]
☄ [tex] \underline{ \underline{ \sf{Provided : }}}[/tex]
- ∠B = 3x°
- ∠ C = 4x°
- ∠ A = 2x°
☄ [tex] \underline{ \sf{To \: Find :}}[/tex]
✏ [tex] \text{Set \: up \: an \: equation \: and \: solve \: for \: x.}[/tex]
[tex] \text{{∠a \: + \: ∠ \: b \: + \: ∠ \: c \: = \: 180 \degree}}[/tex]
→ [tex] \sf{2x + 3x + 4x = 180 \degree}[/tex]
→ [tex] \sf{9x = 180 \degree}[/tex]
→ [tex] \sf{ \frac{9x}{9} = \frac{180 \degree }{9} }[/tex]
→ [tex] \sf{x = 20 \degree}[/tex]
The value of x is 20°. As we are asked to find the measure of ∠C , substituting the value of x in 4x :
[tex] \text{∠c = 4x}[/tex]
→ [tex] \sf{∠ \: c \: = 4 \times 20 \degree}[/tex]
→ [tex] \boxed{ \bold{ \pink{ \sf{∠c \: = 80 \degree}}}}[/tex]
Hence , The measure of ∠ C is 80 °
Hope I helped ! ッ
Have a wonderful day / night ! ♡
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