Question

lesson 4 - 2: do now (day 2)
what is the value of x?
45°
60°
80°
90°

Explanation:

In a triangle, if two sides are equal (as indicated by the tick marks), it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. The sum of angles in a triangle is \(180^{\circ}\). Let the unknown angle be \(x\). We know one angle is \(45^{\circ}\), and since the triangle is isosceles (two equal sides), the angle \(x\) is equal to the angle opposite the other equal - side. Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)), if \(A = 45^{\circ}\) and \(B=x\) and \(C = x\) (because of the isosceles triangle property), then \(45^{\circ}+x + x=180^{\circ}\). But a simpler way is to recognize that in a right - angled isosceles triangle (the given triangle is a right - angled isosceles triangle as it has a \(45^{\circ}\) angle), the two non - right angles are equal. Wait, no, re - checking: the sum of angles in a triangle is \(180^{\circ}\). If we assume it's a right - angled triangle (the unmarked angle is \(90^{\circ}\)), but no, wait the sum of angles: if one angle is \(45^{\circ}\) and the triangle has two equal sides (so two equal angles). Let the two equal angles be \(x\) and \(x\). Then \(45^{\circ}+x + x=180^{\circ}\), \(2x=180 - 45=135^{\circ}\), \(x = 67.5^{\circ}\). But wait, no, looking at the problem again, maybe it's a mis - drawn triangle. Wait, no, wait the options. Wait, another approach: in a triangle, if two sides are equal (isosceles triangle), the base angles are equal. The sum of angles in a triangle is \(180^{\circ}\). If one of the non - equal angles is \(45^{\circ}\), but wait no, the correct approach is: since the triangle has two equal sides (marked by the tick marks), it's an isosceles triangle. The sum of angles in a triangle is \(180^{\circ}\). Let the angles be \(A\), \(B\), \(C\). \(A = 45^{\circ}\), and \(B = C\) (because of equal sides). So \(45^{\circ}+B + C=180^{\circ}\), \(2B=135^{\circ}\), \(B = 67.5^{\circ}\). But this is not in the options. Wait, no, mistake in initial assumption. Wait, the triangle is a right - angled isosceles triangle. The right angle is \(90^{\circ}\), and the other two angles are equal. Using \(A + B + C=180^{\circ}\), \(90^{\circ}+x + x=180^{\circ}\), \(2x=90^{\circ}\), \(x = 45^{\circ}\)

Answer:

\(45^{\circ}\)