Question

medal to the correct answer with an explanation!

Answer 1

ABE and ADE are right triangles, which may help. Look to apply c^2=a^2 + b^2 perhaps.

Answer 2

Since triangles STQ and SRQ are both right triangles, can you conclude they are congruent?

Answer 3

since TQ = QR
can you try to prove triangles TSQ and RSQ as congruent ?

then 2x+13 will be = 21

Answer 4

and you will find angle TSQ as 21
now in triangle TSQ , you know 2 angles, not difficult to find 3rd :)

Answer 5

still confusing

Answer 6

do you know what 'congruent triangles' mean ? or how to prove 2 triangles congruent ?

Answer 7

have you been taught Hypotenuse Leg test for congruency ?
'HL (hypotenuse leg of a right triangle)
Two right triangles are congruent if the hypotenuse and one leg are equal.'

Answer 8

from that does it make sense to conclude, triangles TSQ and RSQ are congruent

Answer 9

yes

Answer 10

then the corresponding angles of those triangles are also congruent, which gives you
angleTSQ = 21

Answer 11

in any triangle, sum of angles = 180
in triangle TSQ,
90 + angle SQT + 21 = 180

just find angle SQT from here

Answer 12

69!

Answer 13

thats one nasty and correct answer you have got! :P