Answer:
110°
Step-by-step explanation:
The consecutive interior angles theorem states that when two parallel lines are cut by a transversal, the pair of angles formed which lie inside the parallel lines on the same side of the transversal are known as consecutive interior angles. This consecutive interior angles are supplementary (that is add up to 180°).
Therefore:
∠4 and ∠6 are consecutive interior angles. Hence:
∠4 + ∠6 = 180° (sum of co-interior angles)
∠4 + 70 = 180
∠4 = 180 - 70
∠4 = 110°
Answer:
25, 50, and 105.
Step-by-step explanation:
Let the first angle be A, the second angle be B, and the third angle be C.
First, the sum of the three angles in a triangle is 180. Thus:
We know that the measure of A is twice the measure of B. Thus:
And the measure of C is 80 more than the measure of B. So:
Let's substitute A and C into the original equation:
Now, let's solve for the second angle (B). Combine like terms:
Subtract 80 from both sides:
Divide both sides by 4:
So, the second angle is 25 degrees.
This means that the first angle is 2(25) or 50 degrees.
And the third angle is 80+25 or 105 degrees.
And we're done!
The angles are 25, 50, and 105.