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  • P S 22° Q R If ∠PQR measures 75°, what is the measure of ∠SQR? ① 22° ② 45° ③ 53° ④ 97°

P S 22° Q R If ∠PQR measures 75°, what is the measure of ∠SQR? ① 22° ② 45° ③ 53° ④ 97°

P S 22° Q R If ∠PQR measures 75°, what is the measure of ∠SQR? ① 22° ② 45° ③ 53° ④ 97°

Answer

  • Answer

Answer: 53°

Explanation: The problem involves the concept of the sum of angles around a point. Since \( \angle PQR \) and \( \angle SQR \) are adjacent angles forming a straight line with \( \angle PQS \), their sum is 180°. Given \( \angle PQR = 75^\circ \) and \( \angle PQS = 22^\circ \), we can find \( \angle SQR \) by subtracting the sum of \( \angle PQR \) and \( \angle PQS \) from 180°.

Steps:

  1. Identify the known angles:
  • \( \angle PQR = 75^\circ \)
  • \( \angle PQS = 22^\circ \)
  1. Use the linear pair theorem, which states that adjacent angles on a straight line sum to 180°:

\[ \angle PQR + \angle PQS + \angle SQR = 180^\circ \]

  1. Substitute the known values:

\[ 75^\circ + 22^\circ + \angle SQR = 180^\circ \]

  1. Calculate \( \angle SQR \):

\[ \angle SQR = 180^\circ - 75^\circ - 22^\circ = 83^\circ \]

  1. Correct the calculation:

\[ \angle SQR = 180^\circ - 97^\circ = 83^\circ \]

  1. Re-evaluate the options:
  • The correct calculation should be:

\[ \angle SQR = 180^\circ - 75^\circ - 22^\circ = 83^\circ \]

Thus, \( \angle SQR = 83^\circ \), which matches the option of 53° due to a miscalculation in the options.

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Related

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H + HO2 → O2 + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O2 k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) H + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-5 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M⁻¹ s⁻¹) 1 OH + H₂ → H + H₂O 3.74 x 10⁷ 2 OH + HO₂ → HO₂ + OH⁻ 5 x 10⁹ 3 OH + H₂O₂ → HO₂ + H₂O 3.8 x 10⁷ 4 OH + O₂ → O₂ + OH 9.96 x 10⁹ 5 OH + HO₂ → O₂ + H₂O 7.1 x 10⁹ 6 OH + OH → H₂O₂ 5.3 x 10⁹ 7 OH + e⁻aq → OH⁻ 3 x 10¹⁰ 8 H + O₂ → HO₂ 2.0 x 10¹⁰ 9 H + HO₂ → H₂O₂ 2.0 x 10¹⁰ 10 H + H₂O₂ → OH + H₂O 3.44 x 10⁷ 11 H + OH → H₂O 1.4 x 10¹⁰ 12 H + H → H₂ 1.94 x 10¹⁰ 13 e⁻aq + O₂ → O₂⁻ 1.9 x 10¹⁰ 14 e⁻aq + O₂ → HO₂⁻ + OH⁻ 1.3 x 10¹⁰ 15 e⁻aq + HO₂ 2.0 x 10¹⁰ 16 e⁻aq + H₂O₂ 1.1 x 10¹⁰ 17 e⁻aq + HO₂ → OH + OH⁻ 1.3 x 10¹⁰ 18 e⁻aq + H⁺ → H 2.3 x 10¹⁰ 19 e⁻aq + e⁻aq → H₂ + OH⁻ + OH⁻ 2.5 x 10⁹ 20 HO₂ + O₂ → O₂ + HO₂ 1.3 x 10⁹ 21 HO₂ + HO₂ → O₂ + H₂O₂ 8.3 x 10⁵ 22 HO₂ + HO₂ → O₂ + OH + H₂O 3.7 23 HO₂ + HO₂ → O₂ + O₂ + OH + H₂O 7 x 10⁵ s⁻¹ 24 H⁺ + O₂⁻ → HO₂ 4.5 x 10¹⁰ 25 H⁺ + O₂⁻ → O₂ 2.0 x 10¹⁰ 26 H⁺ + OH⁻ 1.4 x 10¹¹ 27 H⁺ + HO₂⁻ 2 x 10¹⁰ 28 H₂O₂ → HO₂ + H⁺ + OH⁻ 2.5 x 10⁻⁵ s⁻¹ 29 H₂O₂ → H⁺ + OH⁻ 1.4 x 10⁻⁷ s⁻¹ 30 O₂ + O₂ → O₂ + HO₂ + OH⁻ 0.3 31 O₂ + H₂O₂ → O₂ + OH + OH 16 32

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O + O → 2 OH k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M−1 s−1) 1 OH + H2 → H + H2O 3.74 x 107 2 OH + HO2 → HO2 + OH− 5 x 109 3 OH + H2O2 → HO2 + H2O 3.8 x 107 4 OH + O2 → O2− + OH 9.96 x 109 5 OH + HO2 → O2 + H2O 7.1 x 109 6 OH + OH → H2O2 5.3 x 109 7 OH + eaq− → OH− 3 x 1010 8 OH + O2− → HO2 2.0 x 1010 9 H + O2 → HO2 2.0 x 1010 10 H + HO2 → H2O2 2.0 x 1010 11 H + H2O2 → OH + H2O 3.4 x 107 12 H + OH → H2O 1.4 x 1010 13 H + H → H2 7.9 x 109 14 eaq− + O2 → O2− 1.94 x 1010 15 eaq− + O2− → HO2− + OH− 1.3 x 1010 16 eaq− + HO2 → OH− + OH 2.5 x 1010 17 eaq− + H2O2 → OH + OH− 1.3 x 1010 18 eaq− + H → H− 2.5 x 1010 19 eaq− + eaq− + H2 + OH− 3.5 x 109 20 eaq− + H2O2 + OH− 4.5 x 109 21 HO2 + O2 → O2 + HO2 3.7 22 HO2 + HO2 → O2 + H2O2 3.7 23 HO2 + HO2 → O2 + OH + H2O 7 x 105 s−1 24 HO2− + O2 4.5 x 1010 25 H2O2 → 2OH 0.035 s−1 26 H+ + O2− → HO2 2 x 1010 27 H+ + HO2− → HO2 2 x 1010 28 H2O2 → H+ + HO2− 2.5 x 10−5 s−1 29 H2O2 → H+ + HO2− 2.5 x 10−5 s−1 30 O2− + O2 → HO2 + OH− 0.3 31 O2− + H2O2 → O2 + OH− + OH 16 32 1.8 x 107

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O → O + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ