With these 5 geometry questions! pls 1.)quadrilateral abcd is inscribed in this circle. what is the measure of ∠a ? enter your answer in the box.°2.)quadrilateral abcd is inscribed in a circle. what is the measure of angle a? enter your answer in the box. m∠a= 3.)quadrilateral abcd is inscribed in this circle. what is the measure of angle b? enter your answer in the box. m∠b= °4.)quadrilateral abcd is inscribed in this circle. what is the measure of angle a? enter your answer in the box.°5.) quadrilateral abcd is inscribed in this circle. what is the measure of angle c? enter your answer in the box.°

Figure 1: ⇒ m∠A = 77°

Figure 2: ⇒ m∠A = 59°

Figure 3: ⇒ m∠B = 140°

Figure 4: ⇒ m∠A = 59°

Figure 5: ⇒ m∠C = 92°

Step-by-step explanation:

Figure 1:

∵ ABCD is inscribed quadrilateral in a circle

∴ m∠A + m∠C = 180° ⇒ cyclic quadrilateral

∴ 2x + 9 + 3x + 1 = 180

∴ 5x + 10 = 180 ⇒ ∴5x = 180 - 10 = 170

∴ x = 170 ÷ 5 = 34

∵ m∠A = (2x + 9)°

∴ m∠A = (2 × 34) + 9 = 77°

Figure 2:

∵ ABCD is inscribed quadrilateral in a circle

∴ m∠A + m∠C = 180° ⇒ cyclic quadrilateral

∵ m∠C = 121°

∴ m∠A = 180 - 121 = 59°

Figure 3:

∵ ABCD is inscribed quadrilateral in a circle

∴ m∠B + m∠D = 180° ⇒ cyclic quadrilateral

∴ x + (4x - 20) = 180 ⇒ x + 4x -20 =180

∴ 5x = 180 + 20 = 200

∴ x = 200 ÷ 5 = 40

∴ m∠B = 4 × 40 - 20 = 140°

Figure 4:

∵ ABCD is inscribed quadrilateral in a circle

∴ m∠A + m∠C = 180° ⇒ cyclic quadrilateral

∵ m∠C = 121

∴ m∠A = 180 -121 = 59°

Figure 5:

∵ ABCD is inscribed quadrilateral in a circle

∴ m∠B + m∠D = 180° ⇒ cyclic quadrilateral

∴ x° + 116° = 180°

∴ x = 180° - 116° = 64°

∵ m∠A = 2x - 40

∴ m∠A = 2(64) - 40 = 88°

∵ m∠A + m∠C = 180°

∴ m∠C = 180 - 88 = 92°

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