In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

The angles of a triangle sum to 180°, so m∠S + m∠T = 180° − m∠R. The condition m∠R > m∠S + m∠T therefore gives m∠R > 90°, and hence m∠S + m∠T < 90°. Since both ∠S and ∠T are positive, each is smaller than their sum, so ∠R is greater than both ∠S and ∠T. Thus the true statements are that ∠R is obtuse, the other angles sum to less than 90°, and ∠R exceeds each of them.

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