Answer:
m<PQR = 80°
Step-by-step explanation:
<u>Points to remember</u>
Sum angles in a linear pair is 180
<u>To find the value of x</u>
It is given that, angle PQR and angle RQS are linear pairs, and
m< PQR =5x+5 and m<RQS =11x-65
m<PQR + m<RQS = 180
5x + 5 + 11x - 65 = 180
16x -60 = 180
16x = 180 + 60
16x = 240
x = 15
<u>To find the value of angle PQR</u>
m<PQR = 5x + 5
= 5*15 + 5
= 75 + 5 = 80
Therefore m<PQR = 80°
Sorry we cant see the picture
The diagonals of a parallelogram are congruent
The length WY is 32
<h3>How to determine the length WY</h3>
Given that:
and
Then, we have:
diagonal
Subtract x^2 from both sides
Divide both sides by -6
The length WY is calculated as:
So, we have:
![WY=2 * [x^2 - 48]](https://tex.z-dn.net/?f=WY%3D2%20%2A%20%5Bx%5E2%20-%2048%5D)
Substitute 8 for x
![WY=2 * [8^2 - 48]](https://tex.z-dn.net/?f=WY%3D2%20%2A%20%5B8%5E2%20-%2048%5D)
Simplify
Hence, the length WY is 32
Read more about parallelograms at:
brainly.com/question/10062747
A) Here, sum of two non-adjacent angles: 52 + 25 = 77
Now, ∠3 = 180 - 77 [ sum of all angles in a triangle is 180 ]
so, ∠3 = 103
Now, ∠3 + ∠4 = 180 [ Supplementary angles ]
So, ∠4 = 180 - ∠3
∠4 = 180 - 103 = 77
∠4 = 77 [ which is sum of two non-adjacent angles ]
....Hence proved.
b) m∠4 = 77
[ Solved in previous section ]
Hope this helps!
