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The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is 50o less than that of the largest
angle, then find the largest angle (in degrees).
90
85
80
75
Certainly! Let's break down the solution:
- The angles of a triangle are in an arithmetic progression (AP), so if we let the angles be a−d, a, and a+d, they must add up to 180°.
- Therefore, (a−d)+a+(a+d)=180°.
- Simplifying gives 3a=180°, so a=60°. This is the middle angle.
- The smallest angle is 50° less than the largest angle, so (a−d)=(a+d)−50.
- Substituting a=60 gives (60−d)=(60+d)−50.
- Solving this equation: 60−d=10+d, leads to 2d=50, hence d=25.
- The largest angle is a+d=60+25=85°.
- Correct Answer: Option 2, 85°.
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