SOLUTION: Please help! 1. One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is twice the sum of the first two angles. Find the measure of the

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Question 19349: Please help!
1. One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is twice the sum of the first two angles. Find the measure of the angle in the triangle that has the greatest measure.
A. 90 degree B. 120 degree C. 135 degree D. 140 degree
2. The measure of the vertex angle of any isosceles triangle is 5 degrees less than twice the measure of a base angle. Find the measure of a base angle.
A. 43.75degree B. 46.25 degree C. 87.5 degree D. 92.5 degree
Thanks so much.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
1. One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is twice the sum of the first two angles. Find the measure of the angle in the triangle that has the greatest measure.
A. 90 degree B. 120 degree C. 135 degree D. 140 degree
let smaller angle=x
other angle is 10 more=x+10
sum of these 2 angles=x+x+10=2x+10
twice this =2*(2x+10)=4x+20
sum of all three angles =180=x+x+10+4x+20=6x+30
6x=180-30=150
x=150/6=25
greatest angle =4x+20=4*25+20=120.....so option B is correct
2. The measure of the vertex angle of any isosceles triangle is 5 degrees less than twice the measure of a base angle. Find the measure of a base angle.
let the base angle = x
twice it =2x
5 less=2x-5=vertical angle
sum of 3 angles=x+x+2x-5=180
4x=180+5
4x=185
x=185/4=46.25 degrees...so option B is correct
A. 43.75degree B. 46.25 degree C. 87.5 degree D. 92.5 degree