Make use of the relationships you know about angles inscribed in a circle. You also know the degree measure of a full circle is 360°, so a semicircle is 180°.
13) The sum of the two arcs is 180°, so you have
... (13x -10) + (7x -10) = 180
... 20x -20 = 180
... 20x = 200
... x = 10
Then arc NM is 7·10 -10 = 60 degrees, and angle NLM is half that.
∠NLM = 30°
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14) You know that angle FGH is half the measure of arc FAH, and angle FAH is half the measure of arc FGH. Together these facts tell you
... 2∠FGH + 2∠FAH = arc FAH + arc FGH = 360°
... ∠FGH + ∠FAH = 180° . . . . . opposite angles of an inscribed quadrilateral are supplementary—a nice fact to remember
... (21x -2) + (38x +5) = 180
... 59x = 177 . . . . . . . . . . . . . . collect terms, subtract 3
... x = 3 . . . . . . . . . . . . . . . . . . divide by 59
∠FAH = 38x +5 = 38·3 +5 = 119
Arc FGH has twice this measure: 238°.
