Question

Figure LQPO is a parallelogram.Q65°35°51°0The measure of angle LOQ =oThe measure of angle OPQ =The measure of angle OPL =The measure of angle LQP =The measure of angle LPQ =Blank 1:Blank 2:Blank 3:Blank 4:Blank 5:

Answer 1

The angles at points L and O make up a straight line.

These angles are

`65^o,35^o,51^o\text{ and angle LOQ}`

Angles on a straight line = 180 degrees. So

`\begin{gathered} 65+35+51+angleLOQ=180^o \\ 151+\text{ angle LOQ = 180} \\ \text{LOQ = 180 - 151 = 29}^o \end{gathered}`

Therefore, angle LOQ = 29 degrees

Angle OPQ at point P is opposite to the angle at point L.

The angle at point L = 65 + 35 = 100 degree

Opposite angle of a parallelogram are equal.

Therefore, angle OPQ = 100 degrees

Angle OPL is alternate to angle PLQ. And angle PLQ = 65 degrees

Alternate angles are always equal.

Therefore, angle OPL = 65 degrees

Before we find LQP, let's find LOP.

Recall that LOQ = 29 degrees. So, LOP = 29 + 51 = 80 degrees

LQP is opposite to LOP. Since opposite angles of a parallelogram are equal,

Therefore, LQP = 80 dgrees.

Angle LPQ is alternate to angle OLP. OLP = 35 degrees

Since alternate angles are equal,

Angle LPQ = 35 degrees