In the figure, ray ob bisects ∠toy.
if m∠toy = 8x - 36 and m∠tob = x + 24, what is m∠boy?

Step-by-step explanation:

Look at the picture.

If OB is bisects of ∠TOY, then

m∠TOB = m∠BOY ⇒ m∠TOY = m∠TOB + m∠BOY ⇒ m∠TOY = 2m∠TOB.

We have

m∠TOY = 8x - 36, and m∠TOB = x + 24.

Substitute:

8x - 36 = 2(x + 24)       divdie both sides by 2

4x - 18 = x + 24         add 18 to both sides

4x = x + 42            subtract x from both sides

3x = 42             divide both sides by 3

x = 14

m∠BOY = m∠TOB = x + 24

Put x = 14:

m∠BOY = 14 + 24 = 38

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.