Answer:
<h2>
∠PQT = 72°</h2>
Step-by-step explanation:
According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.
Also from the diagram, ∠OQP + ∠PQT = ∠OQT;
∠PQT = ∠OQT - ∠OQP
Given ∠OQP = 18° and ∠OQT = 90°
∠PQT = 90°-18°
∠PQT = 72°
X = measure of angle 1
y = measure of angle 2
z = measure of angle 3
w = measure of angle 4
Focus on the bottom triangle. The three angles add to 180 degrees
(angle 2) + (angle 3) + 116 = 180
y+z+116 = 180
y+z= 180-116
y+z= 64
Since we have the bottom triangle as isosceles, this means that y = z, so
y+z = 64
y+y = 64
2y = 64
y = 64/2
y = 32
making z = 32 as well
Similarly, angle 1 and angle 4 are 32 degrees because the 116 angle is opposite the top left-most angle, and congruent to this angle. In other words, the bottom triangle is a mirror image of the top triangle.
The figure is a rhombus because all four sides are the same length (as shown by the tickmarks)
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Answer:
This figure is a rhombus
All four angles (angle 1 through angle 4) are the same measure. They are each 32 degrees
Parallel lines will never touch each other while perpendicular forms like an X shape. The slope for the parallel is the same while the perpendicular is a negative reciprocal. (Ex for negative reciprocal. 2/4=4/2)
