Answer:
64 degrees
Step-by-step explanation:
Since the triangles are similar they have the same angle measures
∠P = ∠S ∠R =∠U ∠Q=∠T
We know 2 of the angle measures: ∠S and ∠R, and since they are similar we know ∠P and ∠U
In triangles the sum of all angle measures is always 180 degrees, so we can solve for ∠Q with this formula
subtract 116 from both sides
Therefore ∠Q is equal to 64 degrees
Answer:
A. x=16
Step-by-step explanation:
Similar triangles/ratios
1. Substitute 2x + 7 = 39, 4x + 1 = 65
2. Find size ratio between the two figures, 5:3
3. Check for similarity - 39 x 5/3 = 65
Suppose the length of the card board was x cm by x cm
After squares of 4cm was cut from the corner, the dimension for the box will be:
length=(x-8) cm
width=(x-8) cm
height=4 cm
thus the volume will be:
V=length*width*height
V=4×(x-8)×(x-8)=144
x²-16x+64=36
this can be simplified to form a quadratic equation given by:
x²-16x+28=0
solving the quadratic equation we get:
x=2 or x=14
Thus we conclude that the original dimensions was:
length=14 cm ; width=14 cm
