Question

NO LINKS!!
Please help me with #14 and 15

Answer 1

14) m∠WYZ = 23°

15) m∠ACB = 87°

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 14

According to the SAS Similarity Theorem, triangle VWX and triangle YWV are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠WYZ is the same as m∠WVX.

Angles on a straight line sum to 180°:

`\implies m \angle WYZ + m \angle VYZ = 180^(\circ)`

`\implies (3x-7)^(\circ) + (16x-3)^(\circ) = 180^(\circ)`

`\implies (3x-7) + (16x-3) = 180`

`\implies 3x-7+ 16x-3 = 180`

`\implies 19x-10= 180`

`\implies 19x= 190`

`\implies x=10`

To find the measure of angle WYZ, substitute the found value of x into the expression for the angle:

`\begin{aligned}\implies m \angle WYZ &=(3x-7)^(\circ)\\&=(3(10)-7)^(\circ)\\&=(30-7)^(\circ)\\&=23^(\circ)\end{aligned}`

Therefore, the measure of angle WYZ is 23°.

Question 15

According to the SAS Similarity Theorem, triangle ABC and triangle AED are similar triangles.

If two triangles are similar their corresponding angles are congruent.

Therefore, m∠ABC is equal to m∠AED:

`\implies m \angle AED=m \angle ABC`

`\implies (11x-2)^(\circ)=(6x+13)^(\circ)`

`\implies 11x-2=6x+13`

`\implies 5x=15`

`\implies x = 3`

To find the measure of angle ABC, substitute the found value of x into the expression for the angle:

`\begin{aligned}\implies m \angle ABC&=(6x+13)^(\circ)\\&=(6(3)+13)^(\circ)\\&=(18+13)^(\circ)\\&=31^(\circ)\end{aligned}`

Interior angles of a triangle sum to 180°:

`\implies m \angle ACB + m \angle ABC + m \angle BAC = 180^(\circ)`

`\implies m \angle ACB + 31^(\circ)+ 62^(\circ) = 180^(\circ)`

`\implies m \angle ACB + 93^(\circ) = 180^(\circ)`

`\implies m \angle ACB =87^(\circ)`

Therefore, the measure of angle ACB is 87°.