For lines a, c, and d, line c is parallel to line d and m∠1 = 55°.

Part A: For the given diagram, use the measure of ∠1 to find the measure of the remaining seven angles.
Part B: In two or more complete sentences, explain the relationship between angle pairs a)∠1 and ∠7 and b)∠1 and ∠2. in your explanation, include how you calculated each of the angle measures in the special angle pairs.

m∠1 = 55°, m∠2= 125°, m∠3 = 125°, m∠4 = 55°,

m∠5 = 55°, m∠6 = 125°, m∠7 = 125°, m∠8 = 55°

Solution:

Given m∠1 = 55°.

∠1 and ∠4 are vertically opposite angles.

Vertical angle theorem:

If two lines are intersecting, then vertically opposite angles are congruent.

m∠1 = m∠4

m∠4 = 55°

Sum of the adjacent angles in a straight line = 180°

m∠1 + m∠2 = 180°

55° + m∠2 = 180°

m∠2 = 125°

∠2 and ∠3 are vertically opposite angles.

m∠2 = m∠3

m∠3 = 125°

∠2 and ∠6 are corresponding angles.

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

m∠2 = m∠6

m∠6 = 125°

∠4 and ∠8 are corresponding angles.

m∠4 = m∠8

m∠8 = 55°

∠1 and ∠5 are corresponding angles.

m∠1 = m∠5

m∠5 = 55°

∠3 and ∠7 are corresponding angles.

m∠3 = m∠7

m∠7 = 125°

Hence the measure of angles are

m∠1 = 55°, m∠2= 125°, m∠3 = 125°, m∠4 = 55°,

m∠5 = 55°, m∠6 = 125°, m∠7 = 125°, m∠8 = 55°

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

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