Geometry questions (angles, simliar triangles, polygon)?

Question

Hey, I'm stuck on three geometry questions..

1. Find the measures of two supplementary angles if the measure of the smaller angle is 32 less than the measure of the larger angle.

2. One angle in a right triangle is 42. A second right triangle has an angle with the measure 48. Are the two triangles simliar? (meaning same angles, proportional sides)

3. True or false? A concave polygon can be regular. (all sides and angles congruent)

Thank you so much!

Answer 1

1) x + x+32 = 180
2x + 32 = 180
2x = 148
x = 74, x+32 = 106
The angles are 74 and 106


2) TRUE, since they are right triangles, 42 + 90 subtracted from 180 = 48. By AA, the triangles are similar.



3)A regular polygon has all sides and all angles congruent. A concave one can not be regular.

Answer 2

You should do your homework on your own. Here are some hints:

1. Let one angle be x degrees, then the other is (x-32) degrees. Use the fact that two angles are supplementary if their sum is 180 degrees. REMEMBER TO REPORT BOTH ANGLES AFTER YOU SOLVE FOR x.

2. What is the 3rd angle of the first triangle - use that the sum of 3 angles of a triangle is 180 degrees? Once you have this, use the fact that the triangles will be similar if one of the non-90 degrees can be shown to be equal in both the triangles - this will happen only if the 3rd angle you evaluated turns out to be 48 degrees.

3. I don't remember the definition of a regular polygon, so I can't answer this one.

Answer 3

Supplementary angles add up to 180 degrees, so if one is 32 degrees less than the other, 90-(32/2)=74 degrees, and the other is 116 degrees.

Triangles are only similar if corresponding angles are the same measure, so #2 is false.

Don't know on the last one...

Answer 4

its is a 40 5 40 5 ninety angles qpr and rpq are 40 5 degree angles. yet its chop up into twi triangles making prt 40 5 so prt is a 40 5 40 5 ninety triangles with prt and and tpr ur 40 5 degree angles and ptr is ur ninety degree the facet opp ninety is 3 so s(radical 3)=3 divide via radical 3 s=3/radical 3