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2 years ago

What is the value of X?

Mathematics

1 answer:

natali 33 [55]2 years ago

8 0

Answer: x=8

Step-by-step explanation: Since we know that segment AB and BC are the same measure indicated by the black lines running perpendicular to the lines in triangle themselves, we know that angle A and angle C are the same measure. This means we know this equation... Solve this to complete step 1...

69°=(9y-3)°

If you solve for y, you should get 8. This means that y=8. In knowing that a triangle's interior angles add up to 180°, we know that Angle B must be... Solve this equation for step 2...

∠B=180°-(∠A+∠C)

If you solve to find angle B, you should get that ∠B=42°. Knowing this, we can set up another equation similar to that in step 1 (when we found y knowing the angle) to find x... Solve this equation for your third and final step...

42°=(5x+2)°

If done step 1 through 3 correctly, you should get x to be equal to... and the final answer... x=8

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A pair of tangents to a circle which is inclined to each other at an angle of 60 degree are drawn at ends of two radii. The angl

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The angle between these radii must be 120º.

Step-by-step explanation:

According to Euclidean Geometry, two tangents to a circle are symmetrical to each other and the axis of symmetry passes through the center of the circle and, hence, each tangent is perpendicular to a respective radius. We represent the statement in the diagram included below.

Then, we calculate the angle of the radius with respect to the axis of symmetry by knowing the fact that sum of internal angles within triangle equals 180º. That is to say:

$\theta = 180^{\circ}-90^{\circ}-30^{\circ}$

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And the angle between these two radii is twice the result.

$\theta' = 2\cdot \theta$

$\theta' = 120^{\circ}$

The angle between these radii must be 120º.

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The answer is the second one (B.)

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