Segments CD, GH, and JK intersect at point A. Line AB bisects Line JK. Find the values of a and y

The value of x and y from the figure is 27.5 and 62.5 degrees

To get the value of y, we will take the sum of angle on a straight line JK to have:

22.5 + 130 + x = 180

152.5 + x = 180

x = 180 - 152.5

x = 27.5 degrees

For the angle x, the sum of x and y from the diagram is complementary. Hence;

x + y = 90

y = 90 - x

y = 90 - 27.5

y =  62.5 dgrees

Hence the value of x and y from the figure is 27.5 and 62.5 degrees

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x = 67.5°

y = 27.5°

Step-by-step explanation:

Find x:

m<CAJ = 22.5° (given)

<CAJ and <DAK are vertical angles. Vertical angles are congruent, therefore,

m<DAK = m<CAJ

m<DAK = 22.5° (substitution)

m<BAK = right angle (AB is perpendicular to JK)

Therefore,

m<BAK = 90°

m<DAK + x° = m<BAK (Angle addition postulate)

22.5° + x° = 90° (substitution)

Subtract 22.5 from both sides

x = 90° - 22.5°

x = 67.5°

Find y:

m<CAH = 130° (given)

m<CAH + m<DAK + m<HAK = 180° (Angles on a straight line)

130° + 22.5° + m<HAK = 180° (Substitution)

152.5 + m<HAK = 180°

Subtract 152.5 from both sides

m<HAK = 180° - 152.5°

m<HAK = 27.5°

y = m<HAK (vertical angles are congruent)

y = 27.5° (substitution)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°