INSTRUCTION: Find the size of the angle marked by letters. Pls someone help me please. Help me do letter g and h please. Please ooo I need it right now.

Figure g: x = 52° , y = 19°

Figure h: a = 132° , b = 28°

Step-by-step explanation:

Figure g:

The measure of the pair of linear angles is 180°

The angle of measure 142°, and its adjacent angle which is inscribed angle in the circle are formed a linear pair of angles

∴ The measure of the inscribed angle + 142 = 180

- Subtract 142 from both sides

∴ The measure of the inscribed angle = 38°

The measure of the central angle is twice the measure of the inscribed angle which subtended by the same arc

∴ The measure of the central angel which subtended by the

   same arc with the inscribed angle of measure 38 = 2 × 38

∴ The measure of the central angel = 76°

∵ All the radii in the circle are equal

∵ In Δ which contains the central angle of measure 76 and x

   two side of it are radii

∴ The Δ is an isosceles triangle

∴ The measures of its base angles are x° , x°

∵ The sum of measures of their angles is 180°

∴ x + x + 76 = 180

- Add like terms in the left hand side

∴ 2 x + 76 = 180

- Subtract 76 from both sides

∴ 2 x = 104

- Divide both sides by 2

∴ x = 52

In the Δ whose sides are chords in the circle (large triangle)

∵ This Δ contains angle of measures 38°, (x + y)° , (x + 19)°

∵ x = 52

∵ The sum of the measures of the angles of a Δ is 180°

∴ 38 + (52 + y) + (52 + 19) = 180

- Add the like terms in the left hand side

∴ 161 + y = 180

- Subtract 161 from both sides

∴ y = 19°

Figure h:

The measure of the pair of linear angles is 180°

The angle of measure 132°, and its adjacent angle which is inscribed angle in the circle are formed a linear pair of angles

∴ The measure of the inscribed angle + 132 = 180

- Subtract 132 from both sides

∴ The measure of the inscribed angle = 48°

In any inscribed quadrilateral in the circle the sum of the measure of two opposite angle is 180

∴ a + 48 = 180

- Subtract 48 from both sides

∴ a = 132°

∵ 48° is an inscribed angle subtended by the same arc of the

   central angle at O (opposite to a)

∵ The measure of the central angle is twice the measure of the

    inscribed angle which subtended by the same arc

∴ The measure of the central angle = 2 × 48 = 96°

In the quadrilateral which contains a, 96°, and the other two angles

The sum of the measures of the angles of the quadrilateral is 360°

∴ a + 96 + the sum of the measures of the other 2 angles = 360

∵ a = 132°

∴ 132 + 96 + the sum of the measures of the other 2 angles = 360

- Add the like terms in the left hand side

∴ 228 + the sum of the measures of the other 2 angles = 360

- Subtract 228 from both sides

∴ The sum of the measures of the other 2 angles = 132°

In the inscribed quadrilateral

The sum of the measures of the other 2 angles + a + 20 + b + 48 = 360

∴ 132 + 132 + b + 20 + 48 = 360

- Add the like terms in the left hand side

∴ 332 + b = 360

- Subtract 332 from both sides

∴ b = 28°