If Two Sides of a Triangle Are Unequal, Then the Angle Opposite to the Greater Side Is Greater Than Angle Opposite to the Smaller Side
In the figure...
Question
In the figure given figure, AOB is a straight line. Find the value of x and also answer the following:
iii which angle is obtuse?
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Solution
AOB is straight line. ∴∠AOB=180∘ ∠AOP+∠BOP=180∘ x+30∘+x−30∘=180∘ [Given,∠AOP=x+30∘and∠BOP=x−30∘] 2x=180∘ x=180∘2 ∴x=90∘
Hence, the value of x is 90∘.
Now, ∠AOP=120∘and∠BOP=60∘.
And we know that obtuse angle is greater than 90∘. ∴∠AOP is an obtuse angle.
Hence, ∠AOP is an obtuse angle.