Question

Line PQ bisects angle SPY. SPQ= 11/2 x -5. YPQ= 4x-5/2. Solve for x and find SPY.

A. x= 5/3 and SPY= 8.3
B. x= and 2 SPY= 6
C. x= and 5 SPY= 17.5
D. x= and 91/10 SPY= 90

Answer 1

hey mate here is your answer.

The answer is first option (A) x=5/3

and SPY =8.3.

This is the step by step explanation of the question.

May be helpful for you.

Please mark as a brainliest. ✌ ✌

Answer 2

• X is equal to (5/3) and value of ∠SPY is equal to 8.3 .

Given :-

• PQ bisects ∠SPY .
• ∠SPQ = (11x/2) - 5
• ∠YPQ = 4x - (5/2)

To Find :-

• x = ?
• ∠SPY = ?

Solution :-

since line PQ bisect ∠SPY . It will divide ∠SPY in two equal parts .

So,

→ ∠SPQ = ∠YPQ

putting given values we get,

→ (11x/2) - 5 = 4x - (5/2)

→ 5.5x - 5 = 4x - 2.5

→ 5.5x - 4x = 5 - 2.5

→ 1.5x = 2.5

→ x = (2.5/1.5)

→ x = (25/15)

→ x = (5/3) -------- Equation (1)

now,

→ ∠SPY = ∠SPQ + ∠YPQ

→ ∠SPY = (5.5x - 5) + (4x - 2.5)

→ ∠SPY = 5.5x + 4x - 5 - 2.5

→ ∠SPY = 9.5x - 7.5

putting value of x from Equation (1),

→ ∠SPY = (9.5 × 5)/3 - (7.5)

→ ∠SPY = (47.5/3) - 7.5

→ ∠SPY = (47.5 - 3 × 7.5)/3

→ ∠SPY = (47.5 - 22.5)/3

→ ∠SPY = 25/3

→ ∠SPY ≈ 8.3

Therefore, option (A) x = 5/3 and ∠SPY = 8.3 is correct answer .

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