Question

Just answer what it asks in the picture PLEASE

Answer 1

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.

$\frac{9}{12}=\frac{x}{10}$

Do cross multiplication.

90 = 12x

7.5 = x

Now, to find y:

$\frac{9}{12}=\frac{6}{y}$

Do cross multiplication.

9y = 72

Divide by 9, we get

y = 8

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