Question

The consecutive angles of a parallelogram measure (x +30)° and 4x°. What is the
measure of the smallest angle?

Answer 1

Given:

Consecutive angles of a parallelogram measure (x +30)° and 4x°.

To find:

The smallest angle.

Solution:

Consecutive angles of a parallelogram measure (x +30)° and 4x°.

We know that, sum of two consecutive angles of a parallelogram is 180 degrees.

$(x+30)^\circ+4x^\circ=180^\circ$

$(5x+30)^\circ=180^\circ$

Now,

$5x+30=180$

$5x=180-30$

$5x=150$

Divide both sides by 5.

$x=30$

Now,

One angle: $(30+30)^\circ=60^\circ$

Another angle: $4(30)^\circ=120^\circ$

Therefore, the smallest angle is 60 degrees.