2 intersecting lines are shown. A line with point T, R, W intersects a line with points S, R, V at point R. Clockwise, from the
top left, the angles are (2 x + 10) degrees, blank, blank, (x minus 10) degrees. What is the measure of angle TRV? 20° 50° 60° 130°
2 answers:
Answer:
The measure of angle TRV is 130° ⇒ last answer
Step-by-step explanation:
* <em>According to the attached graph</em>
- Line TRW intersects line SRV at point R
- The measure of angle VRT is (2x + 10)°
- The measure of angle VRW is (x - 10)°
- We need to find measure of angle TRV
- <em>From the attached figure</em>
∵ T , R , W lie on the same line
∴ ∠TRW is a straight angle
- The measure of the straight angle is 180°
∴ m∠TRW = 180°
∵ ∠TRW contains ∠VRT and ∠VRW
∴ m∠VRT + m∠VRW = m∠TRW
∴ m∠VRT + m∠VRW = 180°
∵ m∠VRT = (2x + 10)°
∵ m∠VRW is (x - 10)°
∴ 2x + 10 + x - 10 = 180
- Add like terms
∴ 3x = 180
- Divide both sides by 3
∴ x = 60
∵ m∠TRV = (2x + 10)°
- Substitute x by 60
∴ m∠TRV = 2(60) + 10 = 120 + 10 = 130°
∴ The measure of angle TRV is 130°
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‣ A coin is tossed three times.
‣ The probability of getting,
1) Exactly 3 tails
2) At most 2 heads
3) At least 2 tails
4) Exactly 2 heads
5) Exactly 3 heads
★ When three coins are tossed,
then the sample space = {HHH, HHT, THH, TTH, HTH, HTT, THT, TTT}
[here H denotes head and T denotes tail]
⇒Total number of outcomes = 8
<u>1) Exactly 3 tails </u>
Here
• Favourable outcomes = {HHH} = 1
• Total outcomes = 8
<u>2) At most 2 heads</u>
[It means there can be two or one or no heads]
Here
• Favourable outcomes = {HHT, THH, HTH, TTH, HTT, THT, TTT} = 7
• Total outcomes = 8
<u>3) At least 2 tails </u>
[It means there can be two or more tails]
Here
• Favourable outcomes = {TTH, TTT, HTT, THT} = 4
• Total outcomes = 8
<u>4) Exactly 2 heads </u>
Here
• Favourable outcomes = {HTH, THH, HHT } = 3
• Total outcomes = 8
<u>5) Exactly 3 heads</u>
Here
• Favourable outcomes = {HHH} = 1
• Total outcomes = 8