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Question 1 of 6
In \(\triangle ABC\), \(\angle A = 2\angle B\) and \(\angle C = 3\angle B\). Find \(\angle A\).
Explanation: \(\angle B = x\), \(\angle A = 2x\), \(\angle C = 3x\); \(x+2x+3x=6x=180°\); \(x=30°\); \(\angle A=60°\)
Question 2 of 6
The angles of a triangle are in the ratio \(2:3:5\). Find the largest angle.
Explanation: \(2k+3k+5k=10k=180°\); \(k=18°\); Largest = \(5×18=90°\)
Question 3 of 6
In \(\triangle PQR\), \(PQ = PR\) and \(\angle Q = 70°\). Find \(\angle P\).
Explanation: Isosceles: \(\angle Q = \angle R = 70°\); \(\angle P = 180°-140°=40°\)
Question 4 of 6
Find the measure of each angle of an equilateral triangle.
Explanation: All angles equal: \(180÷3=60°\)
Question 5 of 6
In \(\triangle ABC\), \(AB = AC\) and \(AD\) is the median. If \(\angle BAD = 30°\), find \(\angle BAC\).
Explanation: In isosceles triangle, median to base is also altitude and angle bisector; So \(\angle BAC = 2×30°=60°\)
Question 6 of 6
The hypotenuse of a right triangle is 13 cm and one side is 5 cm. Find the other side.
Explanation: By Pythagoras: \(13^2 = 5^2 + x^2\); \(169=25+x^2\); \(x^2=144\); \(x=12\) cm
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