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[tex]\huge\underline{\tt{\red{Problem:}}}[/tex]
- Find the value of x. Give reasons to justify your solution.
Symbols:
[tex]\quad\quad\quad\quad\tt{ right \: \: angle \: = (a)}[/tex]
[tex]\quad\quad\quad\quad\tt{ interior \: \: angle \: = (b)}[/tex]
[tex]\quad\quad\quad\quad\tt{ exterior \: \: angle \: = (x)}[/tex]
Given that:
[tex]\quad\quad\quad\quad\tt{exterior \: \: angle \: = x+72°}[/tex]
[tex]\quad\quad\quad\quad\tt{ interior \: \: angle \: = 34°}[/tex]
[tex]\quad\quad\quad\quad\tt{ right \: \: angle \: = 90°}[/tex]
Formula:
[tex]\quad\quad\quad\quad\tt{x \: = a + b}[/tex]
Solution:
[tex]\quad\quad\quad\quad\tt{x+72° = 90 ° + 34°}[/tex]
[tex]\quad\quad\quad\quad\tt{x+72° = 124°}[/tex]
[tex]\quad\quad\quad\quad\tt{x = 124° - 72°}[/tex]
[tex]\quad\quad\quad\quad \boxed{\tt{x = 52°}}[/tex]
So, the final answer is:
[tex]\quad\quad\quad\quad \underline{ \color{magenta} \boxed{ \boxed{\tt{ \color{magenta}{x = 52°}}}}}[/tex]
[tex]\huge\underline{\tt{\red{Reason:}}}[/tex]
- We know that an exterior angle is supplementary to interior angle. remember that the exterior angle is equal to the sum of the two opposite interior angles. Suppose that the measure of exterior angle is x + 72° and the measure of two interior angles are 34° with the right angle of 90°. We use (x = a + b) formula. Hence, we have the value of x = 52°. Thats all.
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