Answer
a. 28˚
b. 76˚
c. 104˚
d. 56˚
Step-by-step explanation
Given,
∠BCE=28° ∠ACD=31° & line AB=AC .
According To the Question,
- a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°
- b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚
thus , ∠ABC=76° .
- c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,
Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°
Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)
∠DAB = 180° - 107° ⇔ 73°
& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°
Now, In Triangle ADC Sum of angles in a triangle is 180°
∠ADC = 180° - (31° + 45°) ⇔ 104˚
- d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre
For Diagram, Please Find in Attachment
Answer:
x^2 - y^2) - (x^2 -3x +2)
Step-by-step explanation:
Answer:
LN = 15
Step-by-step explanation:
The arrows on the line segments indicate they are parallel.

<u>Triangle Proportionality Theorem</u>
If a line parallel to one side of a triangle intersects the other two sides of the triangle, then it divides these two sides <u>proportionally</u>.

Given:
⇒ LK = JL - JK = 30 - 18 = 12
Substituting the values into the equation and solving for LN:

Answer:
Step-by-step explanation:
Using the binomial probability relation, the probability that exactly 27 graduates earn a college degree is 0.069
<u>Using the relation</u> :
<em>P(x = x) = nCx * p^x * q^(n-x) </em>
- Probability of success, p = 0.15
- q = 1 - p = 1 - 0.15 = 0.85
- Number of trials, n = 200
- X = 27
<u>Probability of exactly 27 graduates can be defined thus</u> :
P(x = 27) = 200C27 × 0.15^27 × 0.85^173
P(x = 27) = 0.0686264
Therefore, the probability of selecting <em>exactly 27 graduates</em> is 0.069
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