QQuestionMathematics
QuestionMathematics
; Sul AERC ME
2 | Coo oe
5 = EON
hee
| —
re
k a
bi wma a, : \ 4
3 ] Lois SETAE TREN I = ed
Yo ai ; ¥
PRL he ot o
8 days agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Q^1 (a): Identify the given and unknown angles
The diagram shows a cyclic quadrilateral with angles labeled 75°, x, and y. We are to find x and y.
Step 2:Q^1 (a): Use the property of cyclic quadrilaterals
x + 75^{\circ} = 180^{\circ}
Opposite angles in a cyclic quadrilateral sum to 180°.
Step 3:Q^1 (a): Solve for x
x = 180^{\circ} - 75^{\circ} = 105^{\circ}
Subtract 75° from 180° to get x.
Step 4:Q^1 (a): Use the triangle sum property for y
y + 75^{\circ} + 105^{\circ} = 180^{\circ}
Angles in a triangle sum to 180°.
Step 5:Q^1 (a): Solve for y
y = 180^{\circ} - 75^{\circ} - 105^{\circ} = 0^{\circ}
This step is incorrect as per the triangle, so y must be the other angle in the quadrilateral. Use cyclic property: y + (unknown angle) = 180°. Since not all values are visible, leave y as symbolic.
Q^1 (a): Final Answer
x = 105^{\circ}
x is 105°. y cannot be determined without more information.
Step 7:Q^1 (b): Identify the given angle
Angle at PEB is 100°. We are to find angle x at the tangent.
Step 8:Q^1 (b): Use the tangent-chord theorem
x = \angle PEB
The angle between the tangent and chord equals the angle in the alternate segment.
Q^1 (b): Final Answer
x = 100^{\circ}
x is 100° by the tangent-chord theorem.
Step 10:Q^1 (c): Identify the given angles
Angles at Q and S are 35° and 100° respectively. We are to find angle x at the tangent.
Step 11:Q^1 (c): Use the tangent-chord theorem
x = \angle QRS
The angle between the tangent and chord equals the angle in the alternate segment.
Q^1 (c): Final Answer
x = 35^{\circ}
x is 35° by the tangent-chord theorem.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students