Question

I NEED HELP !!! 30 points!!!! and brainliest :)please give sensible answer :(​

Answer 1

Answer:

Step-by-step explanation:

9) PQR Is an isosceles triangle

=> ∠PRQ = (180° - x)/2

PRS is an isosceles right triangle

=> ∠PRS = 45°

Have: ∠PRS + ∠PRQ = 115°

=> $\frac{180-x}{2}+45=115$

=> 180 - x = (115 - 45).2 = 140

<=> x = 180 - 140 = 40

10) ABD is an isosceles right triangle => ∠ABD = 45°

BCD is an equilateral triangle => ∠CBD = 60°

have: x = ∠ABD + ∠CBD = 45° + 60° = 105°

11) have: x = y (2)

PQT is an isosceles triangle => ∠PQT = 180 - 70.2 = 40

QTS   is an isosceles triangle => ∠TQS = 180 -2x

QRS   is an isosceles triangle => ∠RSQ = y

have: 40 + 180 - 2x + y = 180 => 2x - y = 40 (1)

(1)(2) => $\left \{ {{y=x} \atop {2x-y=40}} \right.\\\\=> \left \{ {{x=40} \atop {y=40}} \right.$

=> x + y = 80

12) EFJ Is an equilateral  triangle => ∠FJE = 60

∠FJE is the outer angle of the triangle FHJ but FHJ is an isosceles triangle

=> 60 = 2.∠JHF => ∠JHF = 30°

∠JHF is the outer angle of the triangle FHG

=> 30° = 2x

<=> x = 15°