Answer:
x ≈ 12.6 m
Step-by-step explanation:
By using cosine ratio in the given right triangle RTS,
cos(S)° = 
cos(33)° = 
cos(33)° = 
x = 15.cos(33)°
x = 12.58
x ≈ 12.6 m
Therefore, measure of side ST = 12.6 m is the answer.
Answer:
The angles are 110, 110 and 140
Step-by-step explanation:
Let the equal angles be x.
So we have angles x, x and another third one
Now, the other third angle is 30 degrees larger than x, this means that the other third angle is 30 + x
Since they are angles at a point, adding the three together will make or give 360.
Thus,
x + x + x + 30 = 360
3x + 30 = 360
3x = 360-30
3x = 330
x = 330/3
x = 110
So the other third angle is 110 + 30 = 140
So the angles are 110, 110 and 140
Answer:
B
Step-by-step explanation:
Consider all options:
A. Transformation with the rule

is a reflection across the x-axis.
Reflection across the x-axis preserves the congruence.
B. Transformation with the rule

is a dilation with a scale factor of
over the origin.
Dilation does not preserve the congruence as you get smaller figure.
C. Transformation with the rule

is a translation 6 units to the right and 4 units down.
Translation 6 units to the right and 4 units down preserves the congruence.
D. Transformation with the rule

is a clockwise rotation by
angle over the origin.
Clockwise rotation by
angle over the origin preserves the congruence.
Answer:
A.
Statement: ∠6 ≅ ∠14
Reason: For parallel lines cut by a transversal, corresponding angles are congruent.
Step-by-step explanation:
In the figure attached, a plot of the problem is shown.
Given p || q and r is a transversal which cut p and q, then ∠1 ≅ ∠5 and ∠2 ≅ ∠6.
Given r || s and q is a transversal which cut r and s, then ∠6 ≅ ∠14 and ∠8 ≅ ∠16.
From the picture we see that ∠1 and ∠2 are supplementary, that is, their addition is equal to 180º. ∠2 ≅ ∠6 and ∠6 ≅ ∠14, then ∠2 ≅ ∠14, in consequence ∠1 and ∠14 are supplementary.