Question

The measure of angle 1 is (3x + 10)° In the measure of angle 4 is (4x - 15)°

Answer 1

∠1 = ∠4 ( vertically opposite angles )

Then :-

$3x + 10 = 4x - 15$

$10 = 4x - 15 - 3x$

$10 = 1x - 15$

$1x - 15 = 10$

$1x = 10 + 15$

$1x = 25$

Which means :-

∠1 =

= 3x + 10

= 3 × 25 + 10

= 75 + 10

= 85°

∠4 =

= 4x - 15

= 4 × 25 - 15

= 100 - 15

= 85°

Then :-

∠7 = ∠6

∠6 + ∠4 = 180° ( interior angles on the same side of transversal )

∠6 + 85 = 180°

∠6 = 180 - 85

∠6 = 95°

As ;

∠6 = ∠7

∠7 = 95°

Therefore , angle 7 = 95° .