Themeasureof arc FE is 27degrees,anglem<B is 112degrees, <GHJ = <GIJ = 73⁰ , m<S = 90 degrees in the given circlesThe sum ofanglein the triangle DEF is 180 degreesmFE = <DRecall that <D+<E+<F = 180⁰<D+63+90 = 180<D = 180-153<D = 27 degreesHence themeasureof arc FE is 27degrees6) For this circle geometry, we will use the theoremThe sum of Opposite side of a cyclic quadrilateral is 180 degrees.A + C = 180m<A + 101 = 180m<A = 180-101m<A = 79degreesSimilarlyB + D = 180m<B + 68 = 180m<B = 180-68m<B = 112degrees7) The sum ofanglein a circle is 360, hence;arcGJ+68+31+115 = 36parcGJ = 360 - 214arcGJ = 146⁰Since the angle at the centre is twice angle at the circumference, then;<GHJ = 1/2 arcGJ<GHJ = 1/2(146)<GHJ = 73⁰<GHJ = <GIJ = 73⁰ (angle in the same segment of the circle are equal)8) Recall that the sum of Opposite side of a cyclic quadrilateral is 180 degrees.P + R = 18057 + <R = 180m<R = 180-57m<R = 123degreesSimilarly, m<Q+m<S = 180⁰Since the triangle in a semi circle is a right angled triangle, hence m<Q = 90 degrees (triangle PQR is a right angled triangle)m<S = 180 - 90m<S = 90 degreesTo learn more onCirclesclick:brainly.com/question/11833983#SPJ1...

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