Question

need help solving with working much appreciated

Answer 1

Answer:

i. g = 70°

ii. x = 85°

Step-by-step explanation:

Given:

Let first we name the triangle

i. ) Δ PQR , m∠ PRQ = 40°

ii. ) Δ ABC is a right angle at B and a line B- D-C

       m∠ DAC = 25°

       m∠ ACD = 60°

       m∠ BDA = x°

To Find:

i. g = ?

ii. x = ?

Solution:

i.

In Δ PQR , PR ≅ QR ...........{Given]

∴ Δ PQR is an Isosceles Triangle.

c.........{ Base angles of Isosceles triangle are equal }

∴ m∠ PQR = m∠ RPQ = g

Now sum of all the angles in a triangle is 180°

∴ m∠ PQR + m∠ RPQ + m∠ PRQ = 180°....{Angle sum property of Triangle}

$g + g + 40 = 180\\2g=180-40\\2g=140\\g=\frac{140}{2} \\g=70\°$

∴ g = 70°

ii.

We know sum of all the angles in a triangle is 180°

In Δ DAC

m∠ DAC + m∠ ACD + m∠ ADC = 180°.....{Angle sum property of Triangle}

$25+60+ \angle ADC = 180$

$\angle ADC = 180-85\\\angle ADC =95$

Now By Linear Pair Angle Property

m∠ ADB + m∠ ADC = 180° ........{Linear Pair Angle Property}

$x+95=180\\x=180-95\\x=85$

∴ x = 85°