Question

Help me please!!!!! .

Answer 1

The angle in the first problem measures 67°.

x=16, y=40

Explanation:

1st problem: draw the line r in figure (red) parallel to the two given one and containing the vertex of the angle. The two green angles are congruent since alternate angles from the two parallels t and r when crossed with the upper side of the angle. Same with the two blue angles created by the parallels r and b. The measure of the angle you need is the sum of the two, or 36+31= 67°.

Second problem. The two angles in red are congruent since corresponding angles generated by the parallels m and b and the transversal r. we can then write
`4x-5=3x+11\\`. Solving for x we find x= 16. Now the two angles marked in blue are conjugates when looking at the parallels l and r cut by the transversal m, thus they add up to 180° We know how much the angle with double marks measures (since we found x earlier) so we can write

`(3y+1) + (4*16-5) = 180\\3y+ 1 + 59 = 180\\3y=120 \implies y=40`