Two of the sides of the triangle are congruent, which means that the triangle is isosceles. By the Base Angles Theorem, the angles opposite the congruent sides are also congruent. In other words, their measures must be the same.
6n-3^(∘) = n + 17^(∘)
Let's solve the equation for n.
The diagrams shows a transversal passing through a pair of parallel lines. By the Consecutive Interior Angles Theorem, if two parallel lines are cut by a transversal, the consecutive interior angles are supplementary angles. Since the angles measuring 7x-19^(∘) and 3x+14^(∘) are consecutive interior angles, they must be supplementary.
7x-19^(∘) + 3x+14^(∘) = 180^(∘)
Let's solve the equation above for x.
To find y, let's notice that the angles measuring 5y-2^(∘) and 7x-19^(∘) are vertical angles.
These angles are congruent by the Vertical Angles Theorem. In other words, they have the same measure.
5y-2^(∘) = 7x-19^(∘)
We previously found that x = 18.5^(∘). Let's substitute this value for x and solve the resulting equation for y.
The diagram shows a parallelogram. The angles measuring 3w and 5w+36^(∘) are consecutive angles. There is a theorem that says that if a quadrilateral is a parallelogram, then its consecutive angles are supplementary. This means that the measures of our consecutive angles add up to 180^(∘).
3w+ 5w+36^(∘)=180^(∘)
Let's solve it!
d For any triangle ABC, the Law of Cosines relates the cosine of each angle to the side lengths of the triangle.
Let's use this law to find the value of k. Consider the given triangle.
We know the length of two sides, 25 and 15, and that the measure of their included angle is 120^(∘). We can use substitute this information into the Law of Cosines to write an equation in terms of k.
