Question

NO LINKS!!!
Please help me with #11 and 13

Answer 1

Question 11:

• m∠1 = 35°
• m∠2 = 155°
• m∠4 = 135°
• m∠3 = 55°
• m∠5 = 55°

Question 13:

• x = 15

Explanation:

SAS Similarity Theorem

If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

Question 11

Interior angles of a triangle sum to 180°. Therefore:

`\implies m \angle 3 + 35^(\circ) + 90^(\circ) = 180^(\circ)`

`\implies m \angle 3 + 125^(\circ) = 180^(\circ)`

`\implies m \angle 3 = 55^(\circ)`

If two triangles are similar:

• corresponding angles are congruent.
• corresponding sides are proportional.

According to the SAS Similarity Theorem, the two triangles are similar.

If two triangles are similar, their corresponding angles are congruent.

Therefore:

`\implies m \angle 1 = 35^(\circ)`

`\implies m \angle 5 = m \angle 3 = 55^(\circ)`

Angles on a straight line sum to 180°. Therefore:

`\implies m \angle 1 + m \angle 2 = 180^(\circ)`

`\implies 35^(\circ) + m \angle 2 = 180^(\circ)`

`\implies m \angle 2 = 155^(\circ)`

Similarly:

`\implies m \angle 4 + m \angle 5 = 180^(\circ)`

`\implies m \angle 4 + 55^(\circ) = 180^(\circ)`

`\implies m \angle 4 = 135^(\circ)`

Question 13

According to the SAS Similarity Theorem, the two triangles are similar.

If two triangles are similar, their corresponding angles are congruent.

Angles on a straight line sum to 180°. Therefore:

`\implies (5x - 24)^(\circ) + (8x + 9)^(\circ) = 180^(\circ)`

`\implies (5x - 24) + (8x + 9) = 180`

`\implies 5x - 24 + 8x + 9 = 180`

`\implies 13x - 15 = 180`

`\implies 13x = 195`

`\implies x = 15`