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Find the size of unknown angles

Find the size of unknown angles-example-1
User Thaw De Zin
by
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2 Answers

17 votes
17 votes

Explanation:

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Find the size of unknown angles-example-1
User DylanH
by
3.0k points
25 votes
25 votes

Answer:

Explanation:

2∠0PQ = 36

∠OPQ = 36/2 = 18°

Join OQ,

ΔOPQ is an isosceles triangle as OP = OQ = radius

∠OQP = ∠OPQ {Angles opposite to equal sides are equal}

∠OQP = 18°

∠ORQ = 36

ΔORQ is an isosceles triangle as OR = OQ = radius

∠OQR = ∠ORQ {Angles opposite to equal sides are equal}

∠OQR = 36°

∠PQR = ∠PQO + ∠OQR

= 18 + 36

∠PQR = 54°

∠POR = 2*∠PQR {Central angle theorem}

= 2 * 54

∠POR = 108°

∠PQR + ∠PSR = 180 {Opposite angles of cyclic quadrilateral}

54 + ∠ PSR = 180

∠PSR = 180 - 54

PSR = 126°

∠PSR + ∠RST = 180 {linear pair}

126 + ∠RST = 180

∠RST = 180 - 126

∠RST = 54°

User Vikrant Singh
by
3.3k points