I need help plz i dont understand
1 answer:
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Please consider the attached image for complete question.
We have been given that measure of arc WY is 76° and and measure of arc XZ is 112°. We are asked to find the difference of of the measures of angle WPY and angle XPY.
First of all we will find the measure of angle WPY using intersecting secants theorem. Intersecting secants theorem states that measure of angle formed by two intersecting secants inside a circle is half the sum of intercepting arcs.
We can see that angle WPY and angle XPY are linear angles, so they will add up-to 180 degrees.
Now we need to find difference of both angles as:
Therefore, the difference of the measures of angle WPY and angle XPY is 8 degrees.
Answer:
Angle ACD = 38°
Step-by-step explanation:
The full, correct question is presented the attached image to this solution.
Given
Point O is the centre if the circle
Points A, B, C and D are points on the circle
Angle AOB = 140°
Angle OAC = 14°
Angle AOB = 2 × (Angle ACB) [angle subtended at the centre of the circle is twice the angle subtended at the circumference of the circle)
140° = 2 × (Angle ACB)
Angle ACB = (140°/2) = 70°
(Angle AOB) + (Angle OAB) + (Angle ABO) = 180° [sun of angles in a triangle is 180°]
But Angle OAB = Angle ABO = a [base angles of an iscosceles triangle are equal since OA and OB are both radii for the circle O)
(Angle AOB) + (Angle OAB) + (Angle ABO) = 180°
140° + a + a = 180°
2a = 40°
a = (40/2) = 20°
Angle OAB = Angle ABO = 20°
Angle CAB = (Angle OAC) + (Angle OAB) = 14° + 20° = 34°
Triangle ADC is an iscosceles triangle, hence,
Angle DAC = Angle ACD = x [base angles of an iscosceles triangle are equal]
But
(Angle DCB) + (Angle DAB) = 180° [Opposite angles of a cyclic quadilateral (a quadilateral inscribed in a circle) sum up to give 180°]
Angle DCB = (Angle DCA) + (Angle ACB) = (x + 70°)
Angle DAB = (Angle DAC) + (Angle CAB) = (x + 34°)
(Angle DCB) + (Angle DAB) = 180°
(x + 70°) + (x + 34°) = 180°
2x + 104° = 180°
2x = 180° - 104° = 76°
x = (76°/2) = 38°
Angle DAC = Angle ACD = 38°
Angle ACD = 38°
Hope this Helps!!!
