Question

two angles are vertical and one measures 42°. what is the measure of the other?
48°
90°
138°
42°
question 6
a right triangle has legs measuring 6 cm and 8 cm. what is the length of the hypotenuse?
9 cm
14 cm
10 cm

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal.

Step2: Apply Pythagorean theorem

For a right - triangle with legs \(a = 6\) cm and \(b=8\) cm, the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse.
Substitute \(a = 6\) and \(b = 8\) into the formula: \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}\).

Answer:

For the vertical angles question: \(42^{\circ}\) (the fourth option).
For the right - triangle question: \(10\) cm (the third option).