Answer:
12)x=26.125°
∠P = 115.625°
∠Q =21.125°
∠R=43.25°
13)x=52°
∠L=52°
∠J =45°
∠K =69°
14)x=11°
∠C = 36°
∠D =36°
∠B = 108°
15)x=7
WX = 52
WY=52
XY =29
Step-by-step explanation:
12)In ∆PQR
∠P is 14 less than five times x = 5x-15
∠Q is five less than x=x-5
∠R is nine less than twice x=2x-9
Angle sum property of triangle : The sum of all angles of triangle is 180°
So,5x-15+x-5+2x-9=180
8x-29=180
8x=180+29
x=26.125
So,∠P = 5x-15 =5(26.125)-15=115.625°
∠Q =x-5=26.125-5=21.125°
∠R=2x-9=2(26.125)-9=43.25°
13) In ∆JKL
Let the angle L be x
∠L=x
∠J is seven less than ∠L=x-7
∠K is 21 less than twice ∠L=2x-21
Angle sum property of triangle : The sum of all angles of triangle is 180°
So, x+x-7+2x-21=180°
4x-28=180°
4x=180+28
x=52
∠L=x=52°
∠J =x-7=52-7=45°
∠K =2x-21=2(45)-21=69°
14)In ∆BCD
BC ≅ BD(Given)
Opposite angles of equal sides are equal
So, ∠C =∠D
∠C = 5x – 19
∠D = 2x + 14
So, 5x-19=2x+14
3x=33
x=11
∠C = 5x – 19=5(11)-19=36°
∠D = 2x + 14=2(11)+14=36°
∠B = 13x – 35=13(11)-35=108°
15) In ∆WXY
∠X ≅ ∠Y(Given)
Opposite sides of equal angles are equal
WY=WX
WX = 9x – 11
WY = 7x – 3
So, 9x-11=7x-3
2x=14
x=7
So, WX = 9x – 11=9(7)-11=52
WY=52
XY = 4x + 1=4(7)+1=29