Algebra and polygon angle measures Practice Questions

Warm-upeasy

In parallelogram $PQRS$ , $m\angle P=(4x+6)°$ and $m\angle Q=(2x+24)°$ . What is the measure of $\angle P$ ?

Consecutive angles are supplementary: $(4x+6)+(2x+24)=180$ , so $6x+30=180$ and $x=25$ . Then $m\angle P=4(25)+6=106°$ .

Mid-gameeasy

Each interior angle of rectangle $WXYZ$ measures $(3x-12)°$ . What is the value of $x$ ?

Every interior angle of a rectangle measures $90°$ , so $3x-12=90$ and $x=34$ .

Mid-gameeasy

In $\triangle ABC$ , $m\angle A=(x+8)°$ , $m\angle B=(2x+17)°$ , and $m\angle C=(x+55)°$ . What is the value of $x$ ?

The three interior angles sum to $180°$ : $(x+8)+(2x+17)+(x+55)=180$ , so $4x+80=180$ and $x=25$ .

Mid-gameeasy

Two parallel lines are cut by a transversal. A pair of corresponding angles measure $(3x+16)°$ and $(2x+34)°$ . What is the measure of each of these angles?

Corresponding angles are congruent: $3x+16=2x+34$ , so $x=18$ . Each angle measures $3(18)+16=70°$ .

Mid-gameeasy

Two parallel lines are cut by a transversal. Same-side interior angles measure $(6x-5)°$ and $(4x+15)°$ . What is the value of $x$ ?

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$ , so $10x+10=180$ and $x=17$ .

Mid-gameeasy

Two parallel lines are cut by a transversal. A linear pair of adjacent angles measure $(5x+10)°$ and $(3x+50)°$ . What is the measure of the larger angle?

A linear pair is supplementary: $(5x+10)+(3x+50)=180$ , so $8x+60=180$ and $x=15$ . The angles are $85°$ and $95°$ , so the larger is $95°$ .

Mid-gamemedium

In isosceles $\triangle DEF$ , the vertex angle measures $(4x+10)°$ and each base angle measures $(65-x)°$ . What is the measure of each base angle?

The three angles sum to $180°$ : $2(65-x)+(4x+10)=180$ , so $140+2x=180$ and $x=20$ . Each base angle is $65-20=45°$ .

Buzzer beatermedium

In $\triangle GHI$ , $m\angle G=(2x+5)°$ , $m\angle H=(3x+5)°$ , and $m\angle I=(x+50)°$ . What is the measure of the largest angle of the triangle?

The angles sum to $180°$ : $(2x+5)+(3x+5)+(x+50)=180$ , so $6x+60=180$ and $x=20$ . The angles are $45°$ , $65°$ , and $70°$ , so the largest is $70°$ .

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