Question

1. in the diagram, two parallel lines are cut by a transversal. which of the numbered angles measures 152? 9. reason 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. both angles measure 53°. which of the two types must they be? explain. 10. which two angles have the same measure? 11. lines 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 12. 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 angle - pair relationships

Same - side interior angles formed by two parallel lines and a transversal are supplementary (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: $x=\frac{153}{17}=9$.

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°