In the diagram, the measure of angle R is 53°
Law of sines
From the question, we are to determine the measure of angle R
Using the law of sines, we can write that
[tex]\frac{sin R}{r} =\frac{sin S}{s}[/tex]
In the given diagram,
r = 30
S = 69°
s = 35
Thus,
[tex]\frac{sin R}{30} =\frac{sin 69^\circ}{35}[/tex]
[tex]sin R =\frac{30 \times sin 69^\circ}{35}[/tex]
sin R = 0.8002
R = sin⁻¹(0.8002)
R = 53.149°
R ≈ 53°
Hence, the measure of angle R is 53°
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