Question

in the diagram, two parallel lines are cut by a transversal. which of the numbered angles are congruent? if youre not sure whether a pair of angles formed by two parallel lines and a transversal are same - side exterior angles or alternate exterior angles. such angles measure 53°. which of the two types must they be? explain. what two angles have the same measure? line m and n are parallel. find the following angle pairs in the diagram. if you cant find any, write none. alternate exterior ______ corresponding angles ____ same - side exterior ____ alternate interior ____ same - side interior ____ two angles are same - side interior angles. the measures of the angles are represented by the expressions 7x + 18 and 10x + 9. what are the two angle measures? ______

Explanation:

Step1: Recall same - side interior angles property

Same - side interior angles formed by two parallel lines and a transversal are supplementary, i.e., their sum is 180°. So, we set up the equation $(7x + 18)+(10x + 9)=180$.

Step2: Combine like - terms

Combining the x - terms and the constant terms, we get $7x+10x + 18 + 9=180$, which simplifies to $17x+27 = 180$.

Step3: Solve for x

Subtract 27 from both sides of the equation: $17x=180 - 27=153$. Then divide both sides by 17, so $x=\frac{153}{17}=9$.

Step4: Find the angle measures

For the first angle with measure $7x + 18$, substitute $x = 9$: $7\times9+18=63 + 18=81$. For the second angle with measure $10x + 9$, substitute $x = 9$: $10\times9+9=90 + 9=99$.

Answer:

81 and 99