Question

Drag the tiles to the correct boxes to complete the pairs.

Match the statements with their values.

1.m ∠ABC + m∠BAC + m∠ACB
when ΔABC is an isosceles triangle with

2. m∠ABC when m∠BAC = 70°
and ΔABC is an isosceles triangle with

3. m∠QPR when m∠QRP = 30°
and ΔPQR is an isosceles triangle with

4. m∠BDE when m∠BAC = 45°
and points D and E are the midpoints of
and , respectively, in ΔABC

1. 55°
2. 180°
3. 45°
4. 30°

Answer 1

Part 1) Option 2. 180°

Part 2) Option 1. 55°

Part 3) Option 4. 30°

Part 4) Option 3. 45°

Explanation:

Part 1) Determine

m ∠ABC + m∠BAC + m∠ACB

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In this problem

The sum of the three interior angles of triangle ABC must be equal to 180 degrees

so

m ∠ABC + m∠BAC + m∠ACB=180°

Part 2) Determine m∠ABC

when m∠BAC = 70° and ΔABC is an isosceles triangle with AB=AC

In this problem the vertex angle is m∠BAC = 70°

m∠ABC=m∠ACB ---> because AB=AC

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

2m∠ABC+m∠BAC=180°

substitute the given values

2m∠ABC+70°=180°

2m∠ABC=180°-70°

2m∠ABC=110°

m∠ABC=55°

Part 3) Determine m∠QPR

when m∠QRP = 30° and ΔPQR is an isosceles triangle with PQ=QR

In this problem

m∠QPR=m∠QRP ---> because PQ=QR

we have

m∠QRP = 30° ---> given problem

therefore

m∠QPR = 30°

Part 4) Determine m∠BDE

when m∠BAC = 45° and points D and E are the midpoints of AB and BC in ΔABC

we know that

Segment DE is parallel to segment AC (because the points D and E are the midpoints of segment AB and BC

so

m∠BDE=m∠BAC ----> by corresponding angles

we have

m∠BAC = 45° ---> given problem

therefore

m∠BDE = 45°