To solve this problem, we would have to add the sum of angles in a triangle and then find the missing side. Furthermore, value of R, a and b are 50°, 135° and 130° respectively.
Data;
Sum of Angles in a Triangle
The sum of angles in a triangle is equal to 180° and we can find the missing side on R.
[tex]P+Q+R = 180^0\\85^0+45^0+R = 180^0\\130^0+R=180^0\\R = 180 - 130 \\R = 50^0[/tex]
Since we know the value of R and Q, we can proceed to find a and b.
[tex]Q+ a = 180\\[/tex]
The reason behind this is that the sum of angles on a straight line is equal to 180^0
[tex]45+a = 180 \\a = 180 - 45 \\a = 135^0[/tex]
Now let's find the value of b
[tex]R + b = 180\\R = 50^0\\50 + b = 180\\b = 180 - 50 \\b = 130[/tex]
From the calcuations above, the value of R, a and b are 50°, 135° and 130° respectively.
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