Question

One of the angles formed by two intersecting lines is 50° less than the other one. Find the measure of all angles.

Could somebody please help me ASAP with an explanation?

Answer 1

Two lines while intersecting, form two pairs of vertical angles (see attached diagram). It is known that vertical angles have equal measures.

Thus,

• m∠1=m∠3;
• m∠2=m∠4.

Let m∠1 = x°, then m∠2 = (x+50)°.

Angles 1 and 2 are supplementary, then

x+x+50°=180°,

2x=180°-50°,

2x=130°,

x=65°

Therefore,

• m∠1=65°;
• m∠2=65°+50°=115°.

Answer: 65°, 115°, 65°, 115°