Answer:
8. m∠5 = 160°; m∠8 = 20°
9. BH = 10; CH = 20
10. m∠GBC = 90°
Explanation:
8.
Finding m∠5:
- Angles 1 and 5 are corresponding angles which means they are congruent and have the same measure.
Thus, since m∠1 = m∠5 and m∠1 = 160°, m∠5 also = 160°,
Finding m∠8:
- We see that angle 8 is an exterior angle while angle 5 is an interior angle.
- When an exterior and interior angle lie on the same side of a transversal but on opposite sides of one of the parallel lines, they are supplementary, which means the sum of their measures is 180°.
- Angles 8 and 5 lie on the same side of the traversal t, but on opposite sides of the parallel line n, which means they're supplementary.
Since m∠5 = 160°, we can find m∠8 by subtracting 160 from 180:
m∠5 + m∠8 = 180
m∠8 = 180 - m∠5
m∠8 = 180 - 160
m∠8 = 20
Thus, m∠8 = 20°.
9.
Finding BH and CH:
- A perpendicular bisector splits a triangle into two equal parts and creates two right angles beside each other in both parts.
BH:
- The bisector split side GH entirely which means BG and BH equal each other.
Since BG's length is 10, BH's length is also 10.
CH:
- Since a perpendicular bisector creates two equal halves/parts, the lengths of CG and CH are equal.
Since CG's length is 20, CH's length is also 20.
10.
Finding ∠GBC:
- Sine a perpendicular creates two right angles beside each other, the two right angles are angles GBC and HBC.
Since the measure of a right angle is 90°, m∠GBC = 90°.