91Ó°ÊÓ

$∠\mathbf{1}$and $∠\mathbf{2}$ are supplements.

$∠\mathbf{3}$and $∠\mathbf{4}$ are supplements.

a. If $\mathbf{m}\mathbf{∠}\mathbf{1}\mathbf{=}\mathbf{m}\mathbf{∠}\mathbf{3}\mathbf{=}\mathbf{27}$, find$\mathbf{m}\mathbf{∠}\mathbf{2}$and $\mathbf{m}\mathbf{∠}\mathbf{4}$.

b. If $\mathbf{m}\mathbf{∠}\mathbf{1}\mathbf{=}\mathbf{m}\mathbf{∠}\mathbf{3}\mathbf{=}\mathbf{x}$, find$\mathbf{m}∠\mathbf{2}$and$\mathbf{m}\mathbf{∠}\mathbf{4}$ in terms of x.

c. If two angles are congruent, must their supplements be congruent.

In the diagram, $\stackrel{→}{OB}$bisects $∠AOC$and $\stackrel{↔}{EC}âŠ\yen \stackrel{↔}{OD}$.

Find the value of x.

$m∠1=2x$, $m∠2=6x+2$.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

$a^2>9$if $a>3$.

Can you conclude from the information given for the exercise that $\stackrel{→}{XY}âŠ\yen \stackrel{→}{XZ}$?

$m∠1=m∠2$and$m∠3=m∠4$

Draw any$∠AOB$ and its bisector role="math" localid="1646847955601" $\stackrel{↔}{OE}$. Now draw the rays opposite to $\stackrel{↔}{OA}$,$\stackrel{↔}{OB}$ and $\stackrel{↔}{OE}$. What can you conclude about the part of the diagram shown in red? Prove your conclusion.

In the diagram, $\stackrel{→}{\mathrm{OB}}$bisects $∠\mathbf{AOC}$and $\stackrel{↔}{\mathrm{EC}}âŠ\yen \stackrel{↔}{\mathrm{OD}}$.

Find the value of x.

³¾âˆ 2 = 6x + 9, m∠5 = 2x + 49

Copy everything shown. Complete the proof.

Given:$∠\mathbf{2}â‰\dots ∠\mathbf{3}$

Prove: $\mathbf{∠}\mathbf{1}\mathbf{â‰\dots }\mathbf{∠}\mathbf{4}$

Proof:

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

$x=1$only if $x^2=x$.

In the diagram $\stackrel{→}{OB}$bisects ∠AOC and $\stackrel{↔}{EC}âŠ\yen \stackrel{↔}{OD}$.

Find the value of X.

$m∠2=3x$,$m∠3=2x-4‎$

Copy everything shown and write a two-column proof.
Make a diagram showing$∠PQR$ bisected by role="math" localid="1646848681352" $\stackrel{→}{QX}$. Choose a point Y on the ray opposite to $\stackrel{→}{QX}$.

Prove:$∠PQYâ‰\dots ∠RQY$