Part 1)
we know that
the property of cyclic quadrilaterals for which opposite angles are supplementary
then
m∠A°+43°=180°------------> m∠A=180°-43°=137°
the answer is m∠A=137°
Part 2) <span>Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?
we know that
</span>the property of cyclic quadrilaterals<span> for which opposite angles are supplementary
then:</span>
<span>m∠A+m∠C=<span>180<span>∘
(2x+9)+(3x+1)=180---------------> 5x+10=180
x=(180-10)/5=34
</span></span></span>m∠A=2x+9-------------> 2*34+9=77°
<span>
the answer is </span>m∠A=77°<span>
</span>
Answer:
Measure of arc PQR is 190°
Step-by-step explanation:
First have a sketch of the quadrilateral PQRS inside a circle
You should notice that the intercepted angle is ∠PSR
You should remember that the intercepted arc PQR is twice the intercepted angle ∠PSR
Find the intercepted angle ∠PSR
Remember that in a quadrilateral opposite angles add up to 180°
Hence;
∠PQR+∠PSR=180°
85 + ∠PSR=180°
∠PSR=180°-85°=95°
Find arc PQR
Arc PQR =2×∠PSR
Arc PQR=2×95°
=190°
Answer:
21
Step-by-step explanation:
Substitute the given value into the function and evaluate.
If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees
<em><u>Solution:</u></em>
Given that:
We know that,
Taking cos x as common,
By trignometric functions,
sin 20 = 0.34202
cos 20 = 0.939692
So,
Therefore,
x = arc tan (0.7002)
x = 35 degrees
Therefore value of x is 35 degrees
<h3><u>Method 2:</u></h3>
cos x = sin (20 + x)
sin and cos are co - functions, which means that:
cos x = cos [90 - (20 + x)]
cos x = cos (90 - 20 - x)
cos x = cos (70 - x)
Therefore, x = 70 - x
x + x = 70
2x = 70
x = 35
Therefore value of x is 35 degrees
Answer:
25%
Step-by-step explanation:
3/4 (the probability of drawing a quarter) would equal 75% plus 1/4 (the coin that isnt a quarter) would equal 25% so 75% + 25% = 100%
