Just answer what it asks in the picture PLEASE

m∠1 = 30° (by Vertical angle theorem)

m∠A = 80° (by Triangle sum theorem)

m∠D = 80° (by Triangle sum theorem)

The value of x is 7.5 and y is 9.

Solution:

∠ACB and ∠DCE are vertically opposite angles.

Vertical angle theorem:

If two lines are intersecting, then vertically opposite angles are congruent.

⇒ m∠DCE = m∠ACB

⇒ m∠1 = 30° (by Vertical angle theorem)

In triangle ACD,

Triangle sum property:

Sum of the interior angles of the triangle = 180°

⇒ m∠A + m∠C + m∠B = 180°

⇒ m∠A + 30° + 70° = 180°

⇒ m∠A + 100° = 180°

⇒ m∠A = 100° – 180°

⇒ m∠A = 80° (by Triangle sum theorem)

Similarly, m∠D = 80° (by Triangle sum theorem)

In ΔACD and ΔDCE,

All the angles are congruent, so ΔACD and ΔDCE are similar triangles.

In similar triangle corresponding sides are in the same ratio.

Do cross multiplication.

90 = 12x

7.5 = x

Now, to find y:

Do cross multiplication.

9y = 72

Divide by 9, we get

y = 8

Hence the value of x is 7.5 and y is 9.