please solve these questions it's very tough........
Answers
1) x = 12
2) x = 18°
3) x = 25°
Step-by-step explanation:
1)
GIVEN
Q = 90°
___________________________
TO FIND
x
___________________________
We know that,
Measure of all angles of a triangle is 180°
Therefore,
P + Q + R = 180°
( 3x + 1 )° + 90° + ( 4x + 5 )°
90° + ( 7x + 6 ) = 180°
( 7x + 6 ) = 180° - 90°
( 7x + 6 ) = 90°
7x = 90° - 6
7x = 84°
x = 84 / 7
x = 12
x = 12
___________________________
2)
GIVEN
R = 70°
___________________________
TO FIND
x
___________________________
We know that,
Measure of all angles of a triangle is 180°
Therefore,
P + Q + R = 180°
( x - 10 )° + ( 4x + 30)° + 70° = 180°
( 5x - 10 + 30 )° + 70° = 180°
( 5x + 20 )° + 70° = 180°
( 5x + 20 )° = 180° - 70°
( 5x + 20 )° = 110°
5x = 110° - 20°
5x = 90°
x = 90 / 5
x = 18
x = 18°
___________________________
3)
GIVEN
D = 65°
E = 90°
H = 50°
___________________________
TO FIND
x
___________________________
We know that,
Measure of all angles of a triangle is 180°
Therefore,
D + E + F = 180°
65° + 90° + F = 180°
155° + F = 180°
F = 180° - 155°
F = 25°
We know that,
Measure of all angles of a triangle is 180°
Therefore,
H + G + F = 180°
50° + x + ( 80° + 25° ) = 180°
50° + x + 105 = 180°
155° + x = 180°
x = 180 - 155
x = 25