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3 years ago

Find the measure of each angle in the diagram.

Mathematics

1 answer:

irina1246 [14]3 years ago

7 0

Answer:

10y° = 130°

(4x - 22)° = 50°

(7x + 4)° = 130°

(3y + 11)° = 50°

Step-by-step explanation:

From the picture attached,

Two lines are intersecting each other at a pint making two pairs of vertical angles.

By definition, pair of vertical angles are equal in measure.

10y° = (7x + 4)° [Vertical angles]

-7x + 10y = 4 -----(1)

(3y + 11)° = (4x - 22)° [Vertical angles]

-4x + 3y = -33 ------(2)

[Equation (1) × 3] - [Equation (2) × 10]

(-21x + 30y) - (-40x + 30y) = 12 + 330

-21x + 40x = 342

19x = 342

x = $\frac{342}{19}=18$

From equation (1),

-7(18) + 10y = 4

-126 + 10y = 4

10y = 130

y = 13

Therefore, 10y° = 130°

(4x - 22)° = 50°

(7x + 4)° = 130°

(3y + 11)° = 50°

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