If triangle PQR is an isosceles triangle with PQ = PR, and the vertex angle Q is

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Question: If triangle PQR is an isosceles triangle with PQ = PR, and the vertex angle Q is 40 degrees, what are the base angles?

Options:

Correct Answer: 80 degrees

Solution:

In an isosceles triangle, the base angles are equal. Therefore, the base angles are (180 - 40) / 2 = 70 degrees each.

If triangle PQR is an isosceles triangle with PQ = PR, and the vertex angle Q is 40 degrees, what are the base angles?

If triangle PQR is an isosceles triangle with PQ = PR, and the vertex angle Q is 40 degrees, what are the base angles?

Step 1: Understand that triangle PQR is an isosceles triangle, which means two sides are equal (PQ = PR).
Step 2: Identify that the vertex angle Q is given as 40 degrees.
Step 3: Recall that the sum of all angles in any triangle is always 180 degrees.
Step 4: Since the triangle is isosceles, the two base angles (let's call them angle P and angle R) are equal.
Step 5: Let the measure of each base angle be x degrees. Therefore, we can write the equation: 40 + x + x = 180.
Step 6: Simplify the equation: 40 + 2x = 180.
Step 7: Subtract 40 from both sides: 2x = 180 - 40, which simplifies to 2x = 140.
Step 8: Divide both sides by 2 to find x: x = 140 / 2, which gives x = 70 degrees.
Step 9: Conclude that each base angle (angle P and angle R) is 70 degrees.

Isosceles Triangle Properties – In an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal.
Angle Sum Property of Triangles – The sum of the interior angles of a triangle is always 180 degrees.