PQ=RQ and PSERS. 600
90°
O-
a
P
R
a = [? ]°
Can someone explain please

a = 45°

Step-by-step explanation:

In Δ SPR

∵ PS = RS

∴ Δ SPR is an isosceles triangle

→ In the isosceles triangle, the measures of the base angles are equal

∵ ∠SPR and ∠SRP are the base angle of Δ  SPR

∴ m∠SPR = m∠SRP

∵ m∠SPR = a

∴ m∠SRP = a

∵ In any triangle, the sum of the measures of its interior angles is 180°

∴ m∠SPR + m∠SRP + m∠PSR = 180°

∵ m∠PSR = 90°

→ Substitute m∠SPR and m∠SRP by a each and m∠PSR by 90°

∴ a + a + 90 = 180

→ Add the like terms

∴ 2a + 90 = 180

→ Subtract 90 from both sides

∴ 2a + 90 - 90 = 180 - 90

∴ 2a = 90

→ Divide both sides by 2

∴ a = 45°

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step-by-step explanation: