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QuestionMathematics
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Answer
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Step 1:Q^1 (a): Identify known angles and properties
The diagram shows a cyclic quadrilateral with angles at the circumference. Use the property that opposite angles of a cyclic quadrilateral sum to 180 degrees.
Step 2:Q^1 (a): Write the equation for opposite angles
x + 95^\circ = 180^\circ
Angle x and the given angle 95° are opposite in the cyclic quadrilateral.
Step 3:Q^1 (a): Solve for x
x = 180^\circ - 95^\circ = 85^\circ
Subtract 95° from 180° to find x.
Q^1 (a): Final Answer
x = 85^\circ
The value of the unknown angle x is 85 degrees.
Step 5:Q^1 (b): Identify tangent and chord property
The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
Step 6:Q^1 (b): Relate the angles using the tangent-chord theorem
v = 100^\circ
Angle v is equal to the angle in the alternate segment, which is 100°.
Q^1 (b): Final Answer
v = 100^\circ
The value of the unknown angle v is 100 degrees.
Step 8:Q^1 (c): Identify angles at the circumference
Angles subtended by the same chord at the circumference are equal.
Step 9:Q^1 (c): Relate the angles
y = 35^\circ
Angle y subtended by the same chord as the given 35° angle.
Q^1 (c): Final Answer
y = 35^\circ
The value of the unknown angle y is 35 degrees.
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