Answer:
24°
Step-by-step explanation:
Two angles that form a linear pair are supplementary. That is, their total is 180°.
x° +156° = 180°
x° = 180° -156° = 24°
Given ABCD is a cyclic quadrilateral.
To prove that ∠A + ∠C = 180° and ∠B + ∠D = 180°
Construction: Join AC and BD.
Proof:
<em>Angles in the same segment are equal.</em>
∠ACD = ∠ABD – – – – (1)
∠DAC = ∠DBC – – – – (2)
Add (1) and (2), we get
∠ACD + ∠DAC = ∠ABD + ∠DBC
⇒ ∠ACD + ∠DAC = ∠ABC (Since ∠ABD + ∠DBC = ∠ABC)
Add ∠ADC on both sides.
⇒ ∠ACD + ∠DAC + ∠ADC = ∠ABC + ∠ADC
We know that <em>sum of the angles of a triangle is 180°.</em>
In ΔABC, ∠ACD + ∠DAC + ∠ADC = 180°
Now, 180° = ∠ABC + ∠ADC
180° = ∠B + ∠C – – – – (3)
<em>Sum of all the angles of a quadrilateral = 360°</em>
∠A + ∠B + ∠C + ∠D = 360°
∠A + ∠C + 180° = 360° (using (3))
∠A + ∠C = 360° – 180°
∠A + ∠C = 180° – – – – (4)
Equation (3) and (4) shows that,
Opposite angles of a cyclic quadrilateral are supplementary.
Hence proved.
Answer:
see below
Step-by-step explanation:
-2> x ≥ -7 can be written as -7 ≤ x < -2
-0,5=-1/2
-1/2•(-2)=1
The answer is 1
We know that
Two fractions are equivalent only if the product of the numerator (a) of the first fraction and the denominator (d) of the other fraction is equal to the product of the denominator (b) of the first fraction and the numerator (c<span>) of the other
that means
a/b=c/d-------> a*d=c*b
so
0.34=0.34/1=34/100---------> 0.34/1=34/100
then
0.34*100=1*34-------> 34=34------> fractions (0.34/1) and (34/100) are equivalent
34/100-------> 17//50
34*50=100*17---------> 1700=1700-----> fractions 34/100 and 17/50 are equivalent
the answer is
17/50</span>
