angles across each other at a junction, namely vertical angles, are equal.
so the angles right in the middle, where both triangles intersect, are both equal, that means the triangles have that angle in common as well as the angle x°, meaning both triangles are similar by AA.
if both triangles are similar, that means all their interior angles are the same, meaning y = 75°.
now, let's notice something, those tickmarks, meaning each triangle is an isosceles triangle, which have a vertex angle and twin angles.
since all interior angles in a triangle add up to 180°, so 180 - 75 = 105°, subtracting "y" from the 180°, that leaves 105°, to be split evenly between the twin angles of "x" and the one at the junction.
105/2 = 52.5° = x.
Answer:
85%
Step-by-step explanation:

What I did here was multiply 34/40 by 100 to get 3400/40 or 85%.
Angle CAB is congruent to angle C'A'B'. This is given.
Angle CBA is 56 degrees. This is from the sum of interior angles of a triangle (180 - 41 - 83 = 56)
Angle CBA is congruent angle C'B'A'. Angle CBA is 56 degrees.
Triangle CAB is similar to triangle C'B'A. By the AAA similarity postulate.<span />
Answer:
(d) 71°
Step-by-step explanation:
The desired angle in the given isosceles triangle can be found a couple of ways. The Law of Cosines can be used, or the definition of the sine of an angle can be used.
<h3>Sine</h3>
Since the triangle is isosceles, the bisector of angle W is an altitude of the triangle. The hypotenuse and opposite side with respect to the divided angle are given, so we can use the sine relation.
sin(W/2) = Opposite/Hypotenuse
sin(W/2) = (35/2)/(30) = 7/12
Using the inverse sine function, we find ...
W/2 = arcsin(7/12) ≈ 35.685°
W = 2×36.684° = 71.37°
W ≈ 71°
<h3>Law of cosines</h3>
The law of cosines tells you ...
w² = u² +v² -2uv·cos(W)
Solving for W gives ...
W = arccos((u² +v² -w²)/(2uv))
W = arccos((30² +30² -35²)/(2·30·30)) = arccos(575/1800) ≈ 71.37°
W ≈ 71°
Answer:
71 1/4%
Step-by-step explanation:
I think the change is percentage increase. the method of finding percentage iincrease is increase over percentage increase x 100%