Question

I checked the answer for this question and its. Angle PSR = ⁴⁄₇x = ⁴⁄₇ x 105 = 60°

What I don't understand is how they find the 105°. Could someone write down a step by step explanation answer to this question please?

Answer 1

see explanation

Explanation:

(a)

let ∠ QRS = x then ∠ PQR = x and

∠ QPS =
`(6)/(7)` x and ∠ PSR =
`(4)/(7)` x

the sum of the 4 angles in a quadrilateral = 360°

sum the 4 angles and equate to 360

x + x +
`(6)/(7)` x +
`(4)/(7)` x = 360 ( multiply through by 7 to clear the fractions )

7x + 7x + 6x + 4x = 2520

24x = 2520 ( divide both sides by 24 )

x = 105

then

∠ QRS = 105° , so

∠ PSR =
`(4)/(7)` × 105° = 4 × 15° = 60°

(b)

∠ QPS =
`(6)/(7)` × 105° = 6 × 15° = 90° ← a right angle