Question

Fill in each blank with a true statement. . 4. IF ZAS ZB and the supplement of ZB has measure 22°, then ZA =

Answer 1

Angles are undefined terms in plane geometry.

The true statements are:

• 4. $\angle A = 158$.
• 5. $\angle Q =90$
• 6. $\angle U$ is an obtuse angle
• 7. Its supplement must be an acute angle
• 8. See attachment

Question 4

The first statement is represented as:

$\angle A \cong \angle B$

Supplement of $\angle B = 22^o$

$\angle A \cong \angle B$ means that A and B are congruent.

The supplementary of A and B would be the same

The measure of A is then calculated as:

$\angle A + 22 = 180$

Subtract 22 from both sides

$\angle A = 180 -22$

$\angle A = 158$

Question 5

If LP and LQ are linear pairs, then:

$LP + LQ = 90$

So:

$\angle Q + LP + LQ = 180$

Substitute $LP + LQ = 90$

$\angle Q + 90 = 180$

Subtract 90 from both sides

$\angle Q =- 90 + 180$

$\angle Q =90$

Question 6

$\angle S + \angle T = 90$ --- S and T are supplementary

$\angle T + \angle U = 180$ --- T and U are complementary

Subtract both equations

$\angle S + \angle T - \angle T - \angle U = 90 - 180$

$\angle S - \angle U = -90$

Make U the subject

$\angle U = 90 + \angle S$

This means that:

$\angle U > 90$

Hence,  $\angle U$ is an obtuse angle

Question 7

Obtuse angles are greater than 90 degrees but less than 180.

This means that their supplement must be an acute angle (i.e. less than 90)

Question 8

See attachment

Read more about angles at:

brainly.com/question/13954458